Publications (165)583.87 Total impact
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ABSTRACT: Black hole entropy, denoted by N, in (semi)classical limit is infinite. This scaling reveals a very important information about the qubit degrees of freedom that carry black hole entropy. Namely, the multiplicity of qubits scales as N, whereas their energy gap and their coupling as 1/N. Such a behavior is indeed exhibited by BogoliubovGoldstone degrees of freedom of a quantumcritical state of N soft gravitons (a condensate or a coherent state) describing the black hole quantum portrait. They can be viewed as the Goldstone modes of a broken symmetry acting on the graviton condensate. In this picture Minkowski space naturally emerges as a coherent state of infiniteN gravitons of infinite wavelength and it carries an infinite entropy. In this paper we ask what is the geometric meaning (if any) of the classical limit of this symmetry. We argue that the infiniteN limit of BogoliubovGoldstone modes of critical graviton condensate is described by recentlydiscussed classical BMS supertranslations broken by the black hole geometry. However, the full black hole information can only be recovered for finite N, since the recovery time becomes infinite in classical limit in which N is infinite. 
Article: Black hole solutions in R 2 gravity
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ABSTRACT: We find static spherically symmetric solutions of scale invariant R 2 gravity. The latter has been shown to be equivalent to General Relativity with a positive cosmological constant and a scalar mode. Therefore, one expects that solutions of the R 2 theory will be identical to that of Einstein theory. Indeed, we find that the solutions of R 2 gravity are in onetoone correspondence with solutions of General Relativity in the case of nonvanishing Ricci scalar. However, scalarflat R = 0 solutions are global minima of the R 2 action and they cannot in general be mapped to solutions of the Einstein theory. As we will discuss, the R = 0 solutions arise in Einstein gravity as solutions in the tensionless, strong coupling limit M P → 0. As a further result, there is no corresponding Birkhoff theorem and the Schwarzschild black hole is by no means unique in this framework. In fact, R 2 gravity has a rich structure of vacuum static spherically symmetric solutions partially uncovered here. We also find charged static spherically symmetric backgrounds coupled to a U(1) field. Finally, we provide the entropy and energy formulas for the R 2 theory and we find that entropy and energy vanish for scalarflat backgrounds.  [Show abstract] [Hide abstract]
ABSTRACT: The ${\cal R}^2$ scale invariant gravity theory coupled to conformally invariant matter is investigated. We show that in the nonsupersymmetric case the conformally coupled scalars belong to an $SO(1, 1+n)/SO(1+n)$ manifold, while in the supersymmetric case the scalar manifold becomes isomorphic to the K\"ahlerian space ${\cal M}_n$=$SU(1, 1+n)/ U(1)\times SU(1+n)$. In both cases when the underlying scale symmetry is preserved the vacuum corresponds to de Sitter space. Once the scale symmetry is broken by quantum effects, a transition to flat space becomes possible. We argue that the scale violating terms are induced by anomalies related to a $U(1)_R$ symmetry. The anomaly is resolved via the gauging of a PecceiQuinn axion shift symmetry. The theory describes an inflationary transition from de Sitter to flat Minkowski space, very similar to the Starobinsky inflationary model. The extension to metastable de Sitter superstring vacua is also investigated. The scalar manifold is extended to a much richer manifold, but it contains always ${\cal M}_n$ as a submanifold. In superstrings the metastability is induced by axions that cure the anomalies in chiral $N=1$ (or even $N=0$) supersymmetric vacua via a GreenSchwarz/PecceiQuinn mechanism generalized to four dimensions. We present some typical superstring models and discuss the possible stabilization of the noscale modulus. 
Article: Noncommutative/nonassociative IIA (IIB) geometries from Q and Rbranes and their intersections
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ABSTRACT: In this paper we discuss the construction of nongeometric Q and Rbranes as sources of nongeometric Q and Rfluxes in string compactifications. The nongeometric Qbranes, being obtained via Tduality from the NS 5brane or respectively from the KKmonopole, are still local solutions of the standard NS action, where however the background fields G and B possess nongeometric global monodromy properties. We show that using double field theory and redefined background fields $ \widetilde{G} $ and β as well as their corresponding effective action, the Qbranes are locally and globally well behaved solutions. Furthermore the Rbrane solution can be at least formally constructed using dual coordinates. We derive the associated nongeometric Q and Rfluxes and discuss that closed strings moving in the space transversal to the worldvolumes of the nongeometric branes see a noncommutative or a nonassociative geometry. In the second part of the paper we construct intersecting Q and Rbrane configurations as completely supersymmetric solutions of type IIA/B supergravity with certain SU(3) × SU(3) group structures. In the near horizon limit the intersecting brane configurations lead to type II backgrounds of the form AdS 4 × M 6, where the sixdimensional compact space M 6 is a torus fibration with various nongeometric Q and Rfluxes in the compact directions. It exhibits an interesting noncommutative and nonassociate geometric structure. Furthermore we also determine some of the effective fourdimensional superpotentials originating from the nongeometric fluxes. 
Article: Basic Concepts of String Theory
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ABSTRACT: We discuss the phenomenology and cosmology of a Standardlike Model inspired by string theory, in which the gauge fields are localized on Dbranes wrapping certain compact cycles on an underlying geometry, whose intersection can give rise to chiral fermions. The energy scale associated with string physics is assumed to be near the Planck mass. To develop our program in the simplest way, we work within the construct of a minimal model with gaugeextended sector U(3)B×Sp(1)L×U(1)IR×U(1)L. The resulting U(1) content gauges the baryon number B, the lepton number L, and a third additional Abelian charge IR which acts as the third isospin component of an SU(2)R. All mixing angles and gauge couplings are fixed by rotation of the U(1) gauge fields to a basis diagonal in hypercharge Y and in an anomalyfree linear combination of IR and BL. The anomalous Z′ gauge boson obtains a string scale Stückelberg mass via a 4D version of the GreenSchwarz mechanism. To keep the realization of the Higgs mechanism minimal, we add an extra SU(2) singlet complex scalar, which acquires a VEV and gives a TeVscale mass to the nonanomalous gauge boson Z′′. The model is fully predictive and can be confronted with dijet and dilepton data from LHC8 and, eventually, LHC14. We show that MZ′′≈3–4 TeV saturates current limits from the CMS and ATLAS Collaborations. We also show that for MZ′′≲5 TeV, LHC14 will reach discovery sensitivity ≳5σ. After that, we demonstrate in all generality that Z′′ milliweak interactions could play an important role in observational cosmology. Finally, we examine some phenomenological aspects of the supersymmetric extension of the Dbrane construct.  [Show abstract] [Hide abstract]
ABSTRACT: Type II compactifications with Dbranes and background fluxes are viable candidates to relate string theory to the physics we observe in four dimensions. For simple toroidal orbifold backgrounds the Dbrane and orientifold sector can be described by an exact CFT, but issues such as tadpole cancellation, the GreenSchwarz mechanism, determining the massless spectrum etc. arise in a broader context and can be discussed from the lowenergyeffective action perspective. String compactifications with nonvanishing NSNS and RR pform field strengths provide solutions to the moduli problem, as these background fluxes modify the string equations of motion at leading order so that its solutions generically generate a potential for the wouldbe moduli fields. Thus they receive a vacuum expectation value and a mass. Basic knowledge of \(\mathcal{N} = 1\)supersymmetry in four dimensions is assumed. 
Chapter: The Quantized Fermionic String
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ABSTRACT: The fermionic string is quantized analogously to the bosonic string, though this time leading to a critical dimension d = 10. We first quantize in lightcone gauge and construct the spectrum. To remove the tachyon one has to perform the socalled GSO projection, which guarantees spacetime supersymmetry of the tendimensional theory. There are two possible spacetime supersymmetric GSO projections which result in the type IIA and the type IIB superstring. We also present the covariant path integral quantization. The chapter closes with an appendix on spinors in ddimensions.  [Show abstract] [Hide abstract]
ABSTRACT: As another application of conformal field theory, we want to examine the reparametrization ghosts which we introduced within the path integral quantization of the bosonic string in Chap. 3. In the second part of this chapter we briefly study the very much related issue of BRST quantization of the bosonic string, where we encounter another characterization of physical string states, namely as states in the cohomology of a nilpotent BRST charge. 
Chapter: Theoretical and Mathematical Physics
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ABSTRACT: In the first part of this chapter we compute the oneloop partition function of the closed fermionic string. We will do this in light cone gauge. The possibility to assign to the worldsheet fermions periodic or antiperiodic boundary conditions leads to the concept of spin structures. The requirement of modular invariance is then shown to result in the GSO projection. We also generalize some of the results of Chap. 6 to the case of fermions. We then consider open superstrings, i.e. we extend the formalism of conformal field theories with boundaries to include free fermionic fields. This gives rise to Dbranes in superstring theories. We also discuss nonoriented superstrings, which result form performing a quotient of the type IIB superstring by the worldsheet parity transformation. We show that oneloop diagrams are divergent unless Dbranes are present in the model. This defines the type I superstring, whose construction we discuss in some detail.  [Show abstract] [Hide abstract]
ABSTRACT: So far we discussed the 26dimensional bosonic string and three kinds of 10dimensional superstring theories, the type IIA/B theories and the type I theory. One option to make contact with the fourdimensional world is to compactify the closed string theories on compact spaces. We first study the simplest examples, toroidal compactifications of the bosonic string and the type II superstring theories. These feature a new symmetry, called Tduality. To break supersymmetry, however, one has to compactify on nonflat spaces. The simplest such class are toroidal orbifolds. Moreover, we introduce two additional superstring theories in tendimensions, which are hybrid theories of a rightmoving superstring and a leftmoving bosonic string, whose additional sixteen dimensions are compactified on the weightlattice of \(\mathrm{Spin}(32)/{\mathbb{Z}}_{2}\)or \({E}_{8} \times {E}_{8}\). We then study Dbranes on toroidal spaces and how they transform under Tduality. We introduce intersecting Dbranes, their Tdual images and simple orientifolds on such toroidal spaces. 
Chapter: String Compactifications
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ABSTRACT: In the previous chapter we have learned that in toroidal compactifications of the bosonic string there are, in addition to the KaluzaKlein gauge bosons familiar from field theory, further massless vectors of purely stringy origin. However, we did not show that these massless vectors are gauge bosons of a nonAbelian gauge group G, transforming in the adjoint representation. The necessary mathematical tool to do this is the theory of infinite dimensional (current) algebras, the socalled affine KačMoody algebras. They are the subject of this chapter for which we assume some familiarity with the structure of finite dimensional Lie algebras. 
Chapter: The Quantized Bosonic String
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ABSTRACT: In this chapter the quantization of the bosonic string is discussed. This leads to the notion of a critical dimension (d= 26) in which the bosonic string can consistently propagate. Its discovery was of great importance for the further development of string theory. We will discuss both the quantization in socalled lightcone gauge and the covariant path integral quantization, which leads to the introduction of ghost fields.  [Show abstract] [Hide abstract]
ABSTRACT: In Chap. 4 we have demonstrated the usefulness of conformal field theory as a tool for the bosonic string. In the same way as conformal symmetry was a remnant of the reparametrization invariance of the bosonic string in conformal gauge, superconformal invariance is a remnant of local supersymmetry of the fermionic string in superconformal gauge. This leads us to consider superconformal field theory. In many aspects our discussion of superconformal field theory parallels that of conformal field theory, and we will treat those rather briefly. Of special interest are N = 2 superconformal field theories, as they are related to spacetime supersymmetry. These theories show some new features which we will present in more detail.  [Show abstract] [Hide abstract]
ABSTRACT: To relate string theory to the usual description of particles and their interactions in terms of quantum field theories, it is important to have tools at hand to derive the effective point particle interactions for the massless excitation modes of the string. Such effective actions can be deduced from onshell string scattering amplitudes which are computed as correlation functions of physical state vertex operators. We construct the vertex operators and compute various threepoint functions which are needed to extract e.g. the interactions of graviton, twoform, dilaton and of gauge fields at leading order. We also compute the fourpoint functions of open and closed string tachyons and discuss some of their properties. Often the leading order (in α′) effective actions are already uniquely determined by symmetries, such as gauge symmetries or supersymmetry. We present the bosonic sectors of the tendimensional supergravity theories which are related to the tendimensional superstring theories. We also include a discussion of elevendimensional supergravity. The DiracBornInfeld action, which governs the dynamics of the gauge field on a Dbrane, will also be discussed.  [Show abstract] [Hide abstract]
ABSTRACT: In this chapter we present various conformal field theory constructions which describe string theories in six and four spacetime dimensions. We start with some general comments about strings moving in compactified spaces and then continue our investigation from Sect. 10.5 on strings in orbifold spaces. We then generalize the construction of nonoriented string theories to compact dimensions and discuss the prototype example of an orientifold on the compact space \({T}^{4}/{\mathbb{Z}}_{2}\). In this model we introduce fractional Dbranes to cancel the tadpoles. Next, on a more abstract level, we outline the general structure a CFT must at least have in order to lead to a spacetime supersymmetric compactification. Finally, we provide two concrete four dimensional realizations in terms of certain classes of \(N = 2\)superconformal field theories. The first are the socalled Gepner models and the second are heterotic generalizations of the covariant lattice approach from Chap. 13. 
Chapter: The Classical Bosonic String
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ABSTRACT: Even though we will eventually be interested in a quantum theory of interacting strings, it will turn out to be useful to start two steps back and treat the free classical string. We will set up the Lagrangian formalism which is essential for the path integral quantization which we will treat in Chap. 3. We will then solve the classical equations of motion for single free closed and open strings. These solutions will be used for the canonical quantization which we will discuss in detail in the next chapter.  [Show abstract] [Hide abstract]
ABSTRACT: We reexamine the 10dimensional type II and heterotic superstring theories using the bosonic language. The aim of this bosonic formulation is the construction of the covariant fermion vertex operators, which involves a proper treatment of the \((\beta ,\gamma )\)ghost system, This will in turn lead to the introduction of the socalled covariant lattices.  [Show abstract] [Hide abstract]
ABSTRACT: In this chapter we study issues of relevance for the perturbation theory of oriented bosonic strings. After giving a general description of worldsheets of higher genus, we discuss in some detail string one loop diagrams. We first do this for the closed string leading to torus diagrams, which we discuss both for the bosonic string and, continuing our presentation from Chap. 4, also for abstract conformal field theories. In this context we also present the simple current method, which provides a powerful tool for generating modular invariant partition functions. We also discuss the oneloop amplitude for open strings. From the oneloop amplitude of an open string stretched between two bosonic Dpbranes we extract the Dbrane tension.
Publication Stats
7k  Citations  
583.87  Total Impact Points  
Top Journals
Institutions

19892015

CERN
 Physics Department (PH)
Genève, Geneva, Switzerland


19822015

LudwigMaximiliansUniversity of Munich
 Arnold Sommerfeld Center for Theoretical Physics (ASC)
München, Bavaria, Germany


19852014

Max Planck Institute of Physics
München, Bavaria, Germany


20102011

Technische Universität München
München, Bavaria, Germany


19932005

HumboldtUniversität zu Berlin
 Department of Physics
Berlín, Berlin, Germany


1999

University of California, Santa Barbara
 Kavli Institute for Theoretical Physics
Santa Barbara, California, United States


19861988

California Institute of Technology
Pasadena, California, United States


19831984

University Hospital München
München, Bavaria, Germany
