Jeong-Hyuck Park

Jeong-Hyuck Park
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Jeong-Hyuck verified their affiliation via an institutional email.
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Jeong-Hyuck verified their affiliation via an institutional email.
Sogang University · Department of Physics

Professor / Theoretical Physicist. Ph.D. Cantab

About

142
Publications
29,373
Reads
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3,866
Citations
Additional affiliations
February 2020 - January 2021
Kyoto University
Position
  • Professor
Description
  • On sabbatical leave
February 2013 - January 2014
University of Cambridge
Position
  • Professor
Description
  • Sabbatical
March 2007 - present
Sogang University
Position
  • Faculty Member
Education
September 1994 - July 1995
University of Cambridge
Field of study
  • Theoretical Physics
September 1994 - December 1998
University of Cambridge
Field of study
  • Theoretical Physics
March 1990 - February 1994
Seoul National University
Field of study
  • Physics

Publications

Publications (142)
Cover Page
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Ten-year research summary: what the textbooks don’t tell you about ideal Bose gas
Article
Full-text available
The O(D,D) covariant generalized metric, postulated as a truly fundamental variable, can describe novel geometries where the notion of Riemannian metric ceases to exist. Here we quantize a closed string upon such backgrounds and identify flat, anomaly free, non-Riemannian string vacua in the familiar critical dimension, D=26 (or D=10). Remarkably,...
Article
Full-text available
Admitting non-Riemannian geometries, double field theory extends the notion of spacetime beyond the Riemannian paradigm. We identify a class of singular spacetimes known in general relativity with regular non-Riemannian geometries. The former divergences merely correspond to coordinate singularities of the generalized metric for the latter. Compute...
Preprint
Full-text available
We perform post Newtonian analysis of Double Field Theory taken as the gravitational theory of closed string massless sector. We identify the Eddington-Robertson-Schiff parameters \beta_{PPN}, \gamma_{PPN} with the charges of electric H-flux and dilaton respectively, and further relate them to stress-energy tensor. We show \beta_{PPN}=1 from weak e...
Preprint
Full-text available
We propose a Lorentzian wormhole geometry characterized by a closed string massless sector with nontrivial $H$-flux and a scalar dilaton. In the string frame, the dilaton exhibits a negative kinetic term, enabling the existence of the wormhole. The geometry consists of three distinct regions. The middle region contains the throat, and its boundarie...
Preprint
Full-text available
We propose to solve the dark energy problem by postulating the massless sector of closed strings. This sector constitutes the gravitational multiplet of string theory and, when applied to four-dimensional cosmology, predicts that the expansion of an open Universe defined in string frame is readily accelerating. We confront the prediction with the l...
Article
Full-text available
Modern technology has brought novel types of wealth. In contrast to hard cash, digital currency does not have a physical form. It exists in electronic forms only. To date, it has not been clear what impacts its ongoing growth will have, if any, on wealth distribution. Here, we propose to identify all forms of contemporary wealth into two classes: '...
Preprint
Full-text available
Modern technology has brought novel types of wealth. In contrast to hard cashes, digital currencies do not have a physical form. They exist in electronic forms only. Yet, it has not been clear what impacts their ongoing growth will make, if any, on wealth distribution. Here we propose to identify all forms of contemporary wealth into two classes: '...
Article
Full-text available
We obtained families of generalized van der Waals equations characterized by an even number n = 2, 4, 6 and a continuous free parameter, which is tunable for a critical compressibility factor. Each equation features two adjacent critical points which have a common critical temperature T c and arbitrarily two close critical densities. The critical p...
Preprint
Full-text available
This lecture note surveys the gamma matrices in general dimensions with arbitrary signatures, the study of which is essential to understand the supersymmetry in the corresponding spacetime. The contents supplement the lecture presented by the author at Modave Summer School in Mathematical Physics, Belgium, June, 2005.
Preprint
Full-text available
We obtain families of generalised van der Waals equations characterised by an even number $n=2,4,6$ and a continuous free parameter which is tunable for a critical compressibility factor. Each equation features two adjacent critical points which have a common critical temperature $T_{c}$ and arbitrarily close two critical densities. The critical ph...
Preprint
Full-text available
We initiate a systematic study of fracton physics within the geometric framework of Double Field Theory. We ascribe the immobility and large degeneracy of the former to the non-Riemannian backgrounds of the latter, in terms of generalised geodesics and infinite-dimensional isometries. A doubled pure Yang-Mills or Maxwell theory reduces to an ordina...
Preprint
Full-text available
Admitting non-Riemannian geometries, Double Field Theory extends the notion of spacetime beyond the Riemannian paradigm. We identify a class of singular spacetimes known in General Relativity with regular non-Riemannian geometries. The former divergences merely correspond to coordinate singularities of the generalised metric for the latter. Compute...
Article
Full-text available
A bstract We explore the notion of isometries in non-Riemannian geometries. Such geometries include and generalise the backgrounds of non-relativistic string theory, and they can be naturally described using the formalism of double field theory. Adopting this approach, we first solve the corresponding Killing equations for constant flat non-Riemann...
Preprint
Full-text available
We explore the notion of isometries in non-Riemannian geometries. Such geometries include and generalise the backgrounds of non-relativistic string theory, and they can be naturally described using the formalism of double field theory. Adopting this approach, we first solve the corresponding Killing equations for constant flat non-Riemannian backgr...
Article
Full-text available
In string theory the closed-string massless NS-NS sector forms a multiplet of O(D,D) symmetry. This suggests a specific modification to General Relativity in which the entire NS-NS sector is promoted to stringy graviton fields. Imposing off-shell O(D,D) symmetry fixes the correct couplings to other matter fields and the Einstein field equations are...
Preprint
Full-text available
The $\mathbf{O}(D,D)$ covariant generalized metric, postulated as a truly fundamental variable, can describe novel geometries where the notion of Riemannian metric ceases to exist. Here we quantize a closed string upon such backgrounds and identify flat, anomaly-free, non-Riemannian string vacua in the familiar critical dimension, $D{=26}$ (or $D{=...
Cover Page
Full-text available
What the textbooks don't tell you about ideal Bose gas. First-order or discrete phase transitions of finite systems under constant pressure, without resorting to the thermodynamic limit.
Article
Full-text available
A symmetry principle has been shown to augment unambiguously the Einstein field equations, promoting the whole closed-string massless NS-NS sector to stringy graviton fields. Here we consider its weak field approximation, take a nonrelativistic limit, and derive the stringy augmentation of Newton gravity: ∇2Φ=4πGρ+H·H, ∇·H=0, ∇×H=4πGK. Not only the...
Article
Full-text available
Taking \(\mathbf {O}(D,D)\) covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, \((n,\bar{n})\). Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral...
Article
Full-text available
A bstract The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev-Popov ghosts matches with the graded Poisson geome...
Preprint
Full-text available
A Symmetry Principle has been shown to augment unambiguously the Einstein Field Equations, promoting the whole closed-string massless NS-NS sector to stringy graviton fields. Here we consider its weak field approximation, take a non-relativistic limit, and derive the stringy augmentation of Newton Gravity: \[ \begin{array}{lll} {\bf{\nabla}^{2}\Phi...
Preprint
Full-text available
The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev--Popov ghosts matches with the graded Poisson geometry that...
Preprint
Full-text available
Taking $\mathbf{O}(D,D)$ covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, $(n,\bar{n})$. Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral over...
Preprint
Full-text available
String theory suggests a unique and unambiguous modification to General Relativity: the symmetry of O(D,D) T-duality promotes the entire closed-string massless NS-NS sector to stringy graviton fields. The symmetry fixes the couplings to other matter fields unambiguously and the Einstein field equations are enriched to comprise D^2+1 components, dub...
Preprint
Full-text available
Upon treating the whole closed-string massless NS-NS sector as stringy graviton fields, Double Field Theory may evolve into `Stringy Gravity'. In terms of an $\mathbf{O}(D,D)$ covariant differential geometry beyond Riemann, we present the definitions of the off-shell conserved stringy Einstein curvature tensor and the on-shell conserved stringy Ene...
Article
Full-text available
We propose a novel Kaluza-Klein scheme which assumes the internal space to be maximally non-Riemannian, meaning that no Riemannian metric can be defined for any subspace. Its description is only possible through Double Field Theory but not within supergravity. We spell out the corresponding Scherk-Schwarz twistable Kaluza--Klein ansatz, and point o...
Article
Full-text available
Equation (2.51) in the original article as well as the arXiv versions [v1,v2,v3] contains sign errors.
Preprint
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We propose a novel Kaluza–Klein scheme where no graviscalar moduli can be generated. For this weset the internal space to be maximally non-Riemannian, meaning that no Riemannian metric can bedefined for any subspace. Its description is only possible through Double Field Theory but not withinsupergravity. We spell out the corresponding Scherk–Schwar...
Data
Core idea of Stringy Gravity: Closed string massless sector = Stringy graviton fields
Poster
Full-text available
Core idea: string theory predicts its own gravity rather than GR In General Relativity the metric g_{µν} is the only geometric and gravitational field, whereas in string theory the closed-string massless sector comprises a two-form potential B_{µν} and the string dilaton φ in addition to the metric g_{µν}. Furthermore, these three fields transform...
Article
Full-text available
Upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into Stringy Gravity, i.e. the stringy augmentation of General Relativity. Equipped with an $\mathrm{O}(D,D)$ covariant differential geometry beyond Riemann, we spell out the definition of the Energy-Momentum tensor in Stringy Gravity an...
Preprint
Full-text available
Upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into Stringy Gravity, i.e. the stringy augmentation of General Relativity. Equipped with an O(D, D) covariant differential geometry beyond Riemann, we spell out the definition of the Energy-Momentum tensor in Stringy Gravity and derive i...
Preprint
Upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into Stringy Gravity, i.e. the stringy augmentation of General Relativity. Equipped with an $\mathrm{O}(D,D)$ covariant differential geometry beyond Riemann, we spell out the definition of the Energy-Momentum tensor in Stringy Gravity an...
Article
Full-text available
Dictated by Symmetry Principle, string theory predicts not General Relativity but its own gravity which assumes the entire closed string massless sector to be geometric and thus gravitational. In terms of $R/(MG)$, i.e. the dimensionless radial variable normalized by mass, Stringy Gravity agrees with General Relativity toward infinity, but modifies...
Preprint
Dictated by Symmetry Principle, string theory predicts not General Relativity but its own gravity which assumes the entire closed string massless sector to be geometric and thus gravitational. In terms of $R/(MG)$, i.e. the dimensionless radial variable normalized by mass, Stringy Gravity agrees with General Relativity toward infinity, but modifies...
Article
Full-text available
Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, $(n,\bar{n})$, $0\leq n+\bar{n}\leq D$. Upon thes...
Preprint
Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, $(n,\bar{n})$, $0\leq n+\bar{n}\leq D$. Upon th...
Article
Full-text available
Double Field Theory may suggest to view the whole massless NS-NS sector as the gravitational unity. The doubled diffeomorphisms and the O(D,D) covariance determine unambiguously how the Standard Model as well as a relativistic point particle should couple to the NS-NS sector. The theory also refines the notion of singularity. We consider the most g...
Article
Full-text available
The conventional paradigm for critical phenomena typically assumes the thermodynamic limit in order to achieve non-analyticity. Yet, a counterexample based on the `analyticity' of a finite-system partition function has been suggested. It relies solely on the existence of a spinodal curve and predicts universal values for `isobaric' critical exponen...
Preprint
Full-text available
Finite systems may undergo first or second order phase transitions under not isovolumetric but isobaric condition. The `analyticity' of a finite-system partition function has been argued to imply universal values for isobaric critical exponents, $\alpha_{{\scriptscriptstyle{P}}}$, $\beta_{{\scriptscriptstyle{P}}}$ and $\gamma_{{\scriptscriptstyle{P...
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We construct a world-sheet action for Green-Schwarz superstring in terms of doubled-yet-gauged spacetime coordinates. For an arbitrarily curved NS-NS background, the action possesses $\mathbf{O}(10,10)$ T-duality, $\mathbf{Spin}(1,9)\times\mathbf{Spin}(9,1)$ Lorentz symmetry, coordinate gauge symmetry, spacetime doubled-yet-gauged diffeomorphisms,...
Preprint
We construct a world-sheet action for Green-Schwarz superstring in terms of doubled-yet-gauged spacetime coordinates. For an arbitrarily curved NS-NS background, the action possesses $\mathbf{O}(10,10)$ T-duality, $\mathbf{Spin}(1,9)\times\mathbf{Spin}(9,1)$ Lorentz symmetry, coordinate gauge symmetry, spacetime doubled-yet-gauged diffeomorphisms,...
Preprint
Double Field Theory suggests to view the whole massless sector of closed strings as the gravitational unity. The fundamental symmetries therein, including the $\mathbf{O}(D,D)$ covariance, can determine unambiguously how the Standard Model as well as a relativistic point particle should couple to the closed string massless sector. The theory also r...
Article
Full-text available
We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to O(4,4) T-duality, doubled diffeomorphisms, Spin(1,3) local Lorentz symmetry and, separately, HS(4) higher spin gauge symmetry. We...
Preprint
We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to $\mathbf{O}(4,4)$ T-duality, doubled diffeomorphisms, $\mathbf{Spin}(1,3)$ local Lorentz symmetry and, separately, $\mathbf{H...
Article
Full-text available
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry -- not only globally ('non-geometry'), but even locally ('non-Riemannian'). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri arises precisely as s...
Article
Full-text available
Double field theory is an approach for massless modes of string theory, unifying and geometrizing all gauge invariances in manifest O(D,D) covariant manner. In this approach, we derive off-shell conserved Noether current and corresponding Noether potential associated with unified gauge invariances. We add Wald-type counter two-form to the Noether p...
Article
Full-text available
Double field theory is an approach for massless modes of string theory, unifying and geometrizing all gauge invariances in manifest O(D,D) covariant manner. In this approach, we derive off-shell conserved Noether current and corresponding Noether potential associated with unified gauge invariances. We add Wald-type counter two-form to the Noether p...
Article
Full-text available
We show that, without any extra physical degree introduced, the Standard Model can be readily reformulated as a Double Field Theory. Consequently, the Standard Model can couple to an arbitrary stringy gravitational background in an $\mathbf{O}(4,4)$ T-duality covariant manner and manifests two independent local Lorentz symmetries, $\mathbf{Spin}(1,...
Article
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In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and half-maximal supersymmetric double field theories constructed previously within the so-called semi-covariant form...
Article
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Evading the Mermin-Wagner-Hohenberg no-go theorem and revisiting with rigor the ideal Bose gas confined in a square box, we explore a discrete phase transition in two spatial dimensions. Through both analytic and numerical methods we verify that thermodynamic instability emerges if the number of particles is sufficiently yet finitely large: specifi...
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Appendix of this version delivers the geometric constitution of Double Field Theory, which is chracterized by `doubled-yet-gauged spacetime' and `semi-covariant derivative'.
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Article
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We construct a duality manifest gravitational theory for the special linear group, SL(N) with N ≠ 4. The spacetime is formally extended, to have the dimension \( \frac{1}{2} \)N (N − 1), yet is gauged. Consequently the theory is subject to a section condition. We introduce a semi-covariant derivative and a semi-covariant ‘Riemann’ curvature, both o...
Article
Full-text available
We construct a duality manifest gravitational theory for the special linear group, SL(N) with N\neq 4. The spacetime is formally extended, to have the dimension \frac{1}{2}N(N-1), yet is `gauged'. Consequently the theory is subject to a section condition. We introduce a semi-covariant derivative and a semi-covariant `Riemann' curvature, both of whi...
Article
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We revisit the SL(5) U-duality manifest action constructed by Berman and Perry in an extended spacetime. Upon choosing a four-dimensional solution to the section condition constraint, the theory reduces to a four-dimensional truncation of eleven-dimensional supergravity. In this paper, we show that the theory contains more than this M-theory reduct...
Article
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How many $\mathrm{H_{2}O}$ molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags o...
Article
Full-text available
The section condition in double field theory has been shown to imply that a physical point should be one-to-one identified with a gauge orbit in the doubled coordinate space. Here we show the converse is also true and continue to explore the idea of `spacetime being doubled yet gauged'. Introducing an appropriate gauge connection, we construct a st...
Article
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As the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a `gauge orbit' in the coordinate space. The diffeomorphism symmetry then implies an invariance under arbitrary reparametrizations of...
Article
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Recently Berman and Perry constructed a four-dimensional $ \mathcal{M} $ -theory effective action which manifests SL(5) U-duality. Here we propose an underlying differential geometry of it, under the name ‘SL(5) U-geometry’ which generalizes the ordinary Riemannian geometry in an SL(5) compatible manner. We introduce a ‘semi-covariant’ derivative...
Article
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We construct a supersymmetric extension of double field theory that realizes the ten-dimensional Majorana-Weyl local supersymmetry. In terms of a stringy differential geometry we proposed earlier, our action consists of five simple terms -- two bosonic plus three fermionic -- and manifests not only diffeomorphism and one-form gauge symmetry of B-fi...
Article
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To the full order in fermions, we construct D=10 type II supersymmetric double field theory. We spell the precise N=2 supersymmetry transformation rules as for 32 supercharges. The constructed action unifies type IIA and IIB supergravities in a manifestly covariant manner with respect to O(10,10) T-duality and a pair of local Lorentz groups, or Spi...
Article
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While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry bu...
Article
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In spacetime dimension two, pure Yang-Mills possesses no physical degrees of freedom, and consequently it admits a supersymmetric extension to couple to an arbitrary number, $ \mathcal{N} $ say, of Majorana-Weyl gauginos. This results in $ \left( {\mathcal{N},0} \right) $ super Yang-Mills. Further, its dimensional reduction to mechanics doubles...
Article
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In the name of supersymmetric double field theory, superstring effective actions can be reformulated into simple forms. They feature a pair of vielbeins corresponding to the same spacetime metric, and hence enjoy double local Lorentz symmetries. In a manifestly covariant manner --with regard to O(D,D) T-duality, diffeomorphism, B-field gauge symmet...
Article
Full-text available
We construct a supersymmetric extension of double field theory that realizes the ten-dimensional Majorana-Weyl local supersymmetry. In terms of a stringy differential geometry we proposed earlier, our action consists of five simple terms -- two bosonic plus three fermionic -- and manifests not only diffeomorphism and one-form gauge symmetry of B-fi...
Article
Full-text available
Based on the stringy differential geometry we proposed earlier, we incorporate fermions such as gravitino and dilatino into double field theory in a manifestly covariant manner with regard to O(D,D) T-duality, diffeomorphism, one-form gauge symmetry for B-field and a pair of local Lorentz symmetries. We note that there are two kinds of fermions in...
Article
Full-text available
While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry bu...
Article
Full-text available
We investigate the isobar of an ideal Bose gas confined in a cubic box within the grand canonical ensemble, for a large yet finite number of particles, N. After solving the equation of the spinodal curve, we derive precise formulae for the supercooling and the superheating temperatures which reveal an N^{-1/3} or N^{-1/4} power correction to the kn...
Article
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We explore the phase transitions of the ideal relativistic neutral Bose gas confined in a cubic box, without assuming the thermodynamic limit nor continuous approximation. While the corresponding non-relativistic canonical partition function is essentially a one-variable function depending on a particular combination of temperature and volume, the...
Article
Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manif...
Article
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We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both i...
Article
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In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D,D) rotation. In this paper, we conceive a differential geometry characterized by a O(D,D) symmetric projection, as th...
Article
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We consider supersymmetric extensions of a recently proposed partonic description of a bosonic p-brane which reformulates the Nambu-Goto action as an interacting multi-particle action with Filippov-Lie algebra gauge symmetry. We construct a worldline supersymmetric action by postulating, among others, a p-form fermion. Demanding a local worldline s...
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We continue our study of BPS equations and supersymmetric configurations in the Bagger–Lambert (BL) theory. The superalgebra allows three different types of central extensions which correspond to compounds of various M-theory objects: M2-branes, M5-branes, gravity waves and Kaluza–Klein monopoles which intersect or have overlaps with the M2-branes...
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We propose a novel prescription to take off the square root of Nambu-Goto action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker or also known as Polyakov method. With an arbitrary decomposition as d+n=p+1, our resulting action is a modified d-dimensional Polyakov action which is gauged and possesses a Nambu n-bracket squared pote...
Article
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While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in eleven dimensions, which is invariant under global supersymmetry, local fermionic symmetry and worldvolume diffeom...
Article
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We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total Hamiltonian systems. In particular, in analogue to total Hamiltonians, we introduce the notion of total Noeth...
Preprint
We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total Hamiltonian systems. In particular, in analogue to total Hamiltonians, we introduce the notion of total Noeth...

Questions

Question (1)
Question
Here `water' means a collection of the molecules which can actually `boil', i.e. able to feature a liquid-gas phase transition. I believe the answer should be a finite number rather than infinity; cf. the definite answer for an ideal gas from the publication below.

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