[Show abstract][Hide abstract] ABSTRACT: We use localization techniques to calculate the Euclidean partition functions for \( \mathcal{N} \) = 1 theories on four-dimensional manifolds M of the form S
1× M
3, where M
3 is a circle bundle over a Riemann surface. These are generalizations of the \( \mathcal{N} \) = 1 indices in four-dimensions including the lens space index. We show that these generalized indices are holomorphic functions of the complex structure moduli on M. We exhibit the deformation by background flat connection.
Journal of High Energy Physics 12/2014; 2014(12). DOI:10.1007/JHEP12(2014)150 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We use localization techniques to calculate the Euclidean partition functions
for $\mathcal{N}=1$ theories on four-dimensional manifolds $M$ of the form $S^1
\times M_3$, where $M_3$ is a circle bundle over a Riemann surface. These are
generalizations of the $\mathcal{N}=1$ indices in four-dimensions including the
lens space index. We show that these generalized indices are holomorphic
functions of the complex structure moduli on $M$. We exhibit the deformation by
background flat connections and the insertion of supersymmetric Wilson loops.
[Show abstract][Hide abstract] ABSTRACT: Supersymmetric Renyi entropies are defined for three-dimensional N=2
superconformal field theories on a branched covering of a three-sphere by using
the localized partition functions. Under a conformal transformation, the
branched covering is mapped to S^1 x H^2, whose gravity dual is the charged
topological AdS4 black hole. The black hole can be embedded into
four-dimensional N=2 gauged supergravity where the mass and charge are related
so that it preserves half of the supersymmetries. We compute the supersymmetric
Renyi entropies with and without a certain type of Wilson loop operators in the
gravity theory. We find they agree with those of the dual field theories in the
large-N limit.
Journal of High Energy Physics 01/2014; 2014(7). DOI:10.1007/JHEP07(2014)061 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider 3d N>= 2 superconformal field theories on a branched covering of
a three-sphere. The Renyi entropy of a CFT is given by the partition function
on this space, but conical singularities break the supersymmetry preserved in
the bulk. We turn on a compensating R-symmetry gauge field and compute the
partition function using localization. We define a supersymmetric observable,
called the super Renyi entropy, parametrized by a real number q. We show that
the super Renyi entropy is duality invariant and reduces to entanglement
entropy in the q -> 1 limit. We provide some examples.
Journal of High Energy Physics 06/2013; 2013(10). DOI:10.1007/JHEP10(2013)155 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The coefficient tau_{RR} of the two-point function of the superconformal
U(1)_R currents of N=2 SCFTs in three-dimensions is recently shown to be
obtained by differentiating the partition function on a squashed three-sphere
with respect to the squashing parameter. With this method, we compute the
tau_{RR} for N=2 Wess-Zumino models and SQCD numerically for small number of
flavors and analytically in the large number limit. We study the behavior of
tau_{RR} under an RG flow by adding superpotentials to the theories. While the
tau_{RR} decreases for the gauge theories, we find an N=2 Wess-Zumino model
whose tau_{RR} increases along the RG flow. Since tau_{RR} is proportional to
the coefficient C_T of the two-point correlation function of the stress-energy
tensors for N=2 superconformal field theories, this rules out the possibility
of C_T being a measure of the degrees of freedom which monotonically decreases
along RG flows in three-dimensions.
Journal of High Energy Physics 03/2013; 2013(5). DOI:10.1007/JHEP05(2013)165 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The Renyi entropies of a massless Dirac fermion on a circle with chemical
potential are calculated analytically at nonzero temperature by using the
bosonization method. The bosonization of a massive Dirac fermion to the
sine-Gordon model lets us obtain the small mass corrections to the entropies.
We numerically compute the Renyi entropies by putting a massive fermion on the
lattice and find agreement between the analytic and numerical results. In the
presence of a mass gap, we show that corrections to Renyi and entanglement
entropies in the limit m >> T scale as exp(-m/T). We also show that when there
is ground state degeneracy in the gapless case, the limits m to zero and T to
zero do not commute.
Journal of High Energy Physics 01/2013; 2013(3). DOI:10.1007/JHEP03(2013)077 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study quantum quench in a holographic model of a zero temperature
insulator-superfluid transition. The model is a modification of that of
arXiv:0911.0962 and involves a self-coupled complex scalar field, Einstein
gravity with a negative cosmological constant, and Maxwell field with one of
the spatial directions compact. In a suitable regime of parameters, the scalar
field can be treated as a probe field whose backreaction to both the metric and
the gauge field can be ignored. We show that when the chemical potential of the
dual field theory lies between two critical values, the equilibrium background
geometry is a AdS soliton with a constant gauge field, while the complex scalar
condenses leading to broken symmetry. We then turn on a time dependent source
for the order parameter which interpolates between constant values and crosses
the order-disorder critical point. In the critical region adiabaticity breaks
down, but for a small rate of change of the source $v$ there is a new small-$v$
expansion in fractional powers of $v$. The resulting critical dynamics is
dominated by a zero mode of the bulk field. To lowest order in this small-$v$
expansion, the order parameter satisfies a time dependent Landau-Ginsburg
equation which has $z=2$, but non-dissipative. These predictions are verified
by explicit numerical solutions of the bulk equations of motion.
Journal of High Energy Physics 11/2012; 2013(3). DOI:10.1007/JHEP03(2013)146 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We compute the 4d superconformal index for N=1, 2 gauge theories on S1×L(p,1), where L(p,1) is a lens space. We find that the 4d N=1, 2 index on S1×L(p,1) reduces to a 3d N=2, 4 index on S1×S2 in the large p limit, and to a 3d partition function on a squashed L(p,1) when the size of the temporal S1 shrinks to zero. As an application of our index, we study 4d N=2 superconformal field theories arising from the 6d N=(2,0) A1 theory on a punctured Riemann surface Σ, and conjecture the existence of a 2d topological quantum field theory on Σ whose correlation function coincides with the 4d N=2 index on S1×L(p,1).
[Show abstract][Hide abstract] ABSTRACT: The renormalized entanglement entropy (REE) across a circle of radius R has
been proposed as a c-function in Poincar\'e invariant (2+1)-dimensional field
theory. A proof has been presented of its monotonic behavior as a function of
R, based on the strong subadditivity of entanglement entropy. However, this
proof does not directly establish stationarity of REE at conformal fixed points
of the renormalization group. In this note we study the REE for the free
massive scalar field theory near the UV fixed point described by a massless
scalar. Our numerical calculation indicates that the REE is not stationary at
the UV fixed point.
Journal of High Energy Physics 07/2012; 2012(10). DOI:10.1007/JHEP10(2012)058 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We use a mix of field theoretic and holographic techniques to elucidate
various properties of quantum entanglement entropy. In (3+1)-dimensional
conformal field theory we study the divergent terms in the entropy when the
entangling surface has a conical or a wedge singularity. In (2+1)-dimensional
field theory with a mass gap we calculate, for an arbitrary smooth entanglement
contour, the expansion of the entropy in inverse odd powers of the mass. We
show that the shape-dependent coefficients that arise are even powers of the
extrinsic curvature and its derivatives. A useful dual construction of a
(2+1)-dimensional theory, which allows us to exhibit these properties, is
provided by the CGLP background. This smooth warped throat solution of
11-dimensional supergravity describes renormalization group flow from a
conformal field theory in the UV to a gapped one in the IR. For this flow we
calculate the recently introduced renormalized entanglement entropy and confirm
that it is a monotonic function.
Journal of High Energy Physics 04/2012; 2012(7). DOI:10.1007/JHEP07(2012)001 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider N = 3 supersymmetric Chern-Simons gauge theories with product
unitary and orthosymplectic groups and bifundamental and fundamental fields. We
study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov
matrix model. The saddlepoint equations in a large N limit lead to a constraint
that the long range forces between the eigenvalues must cancel; the resulting
quiver theories are of affine Dynkin type. We introduce a folding/unfolding
trick which lets us, at the level of the large N matrix model, (i) map quivers
with orthosymplectic groups to those with unitary groups, and (ii) obtain
non-simply laced quivers from the corresponding simply laced quivers using a
Z_2 outer automorphism. The brane configurations of the quivers are described
in string theory and the folding/unfolding is interpreted as the
addition/subtraction of orientifold and orbifold planes. We also relate the
U(N) quiver theories to the affine ADE quiver matrix models with a
Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in
2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.
Journal of High Energy Physics 01/2012; 2012(4). DOI:10.1007/JHEP04(2012)138 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We propose that N M5-branes, put on R4/Zm with deformation parameters ϵ1,2, realize two-dimensional theory with SÛ(m)N symmetry and mth para-WN symmetry. This includes the standard WN symmetry for m=1 and super-Viraroro symmetry for m=N=2. We provide a small check of this proposal by calculating the central charge of the 2D theory from the anomaly polynomial of the 6D theory.
[Show abstract][Hide abstract] ABSTRACT: For (3+1)-dimensional fermions, a net axial charge and external magnetic
field can lead to a current parallel to the magnetic field. This is the chiral
magnetic effect. We use gauge-gravity duality to study the chiral magnetic
effect in large-Nc, strongly-coupled N=4 supersymmetric SU(Nc) Yang-Mills
theory coupled to a number Nf << Nc of N=2 hypermultiplets in the Nc
representation of SU(Nc), i.e. flavor fields. Specifically, we introduce an
external magnetic field and a time-dependent phase for the mass of the flavor
fields, which is equivalent to an axial chemical potential for the flavor
fermions, and we compute holographically the resulting chiral magnetic current.
For massless flavors we find that the current takes the value determined by the
axial anomaly. For massive flavors the current appears only in the presence of
a condensate of pseudo-scalar mesons, and has a smaller value than for massless
flavors, dropping to zero for sufficiently large mass or magnetic field. The
axial symmetry in our system is part of the R-symmetry, and the states we study
involve a net flow of axial charge to the adjoint sector from an external
source coupled to the flavors. We compute the time rate of change of axial
charge and of energy both in field theory and from holography, with perfect
agreement. In contrast to previous holographic models of the chiral magnetic
effect, in our system the vector current is conserved and gauge-invariant
without any special counterterms.
Journal of High Energy Physics 06/2011; 10(10). DOI:10.1007/JHEP10(2011)084 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We compute the partition function on S^3 of 3d N=4 theories which arise as
the low-energy limit of 4d N=4 super Yang-Mills theory on a segment or on a
junction, and propose its 1d interpretation. We show that the partition
function can be written as an overlap of wavefunctions determined by the
boundary conditions. We also comment on the connection of our results with the
4d superconformal index and the 2d q-deformed Yang-Mills theory.
Journal of High Energy Physics 05/2011; 2011(8). DOI:10.1007/JHEP08(2011)003 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We construct Lifshitz-like Janus solutions in the Einstein-scalar theory with
cosmological constant in arbitrary dimensions. They are holographically dual to
z=2 Lifshitz-like field theories with a defect. The four-dimensional solutions
can be embedded into type IIB supergravity as dilatonic deformations of AdS_5 x
Y^5 with three-form field strengths, where Y^5 is a five-dimensional Einstein
manifold.
Journal of High Energy Physics 10/2010; 2011(2). DOI:10.1007/JHEP02(2011)023 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The extremal Kerr black hole with the angular momentum J is conjectured to be
dual to CFT with central charges c_L=c_R=12J. However, the central charge in
the right sector remains to be explicitly derived so far. In order to
investigate this issue, we introduce new near horizon limits of (near) extremal
Kerr and five-dimensional Myers-Perry black holes. We obtain Virasoro algebras
as asymptotic symmetries and calculate the central charges associated with
them. One of them is equivalent to that of the previous studies, and the other
is non-zero, but still the order of near extremal parameter. Redefining the
algebras to take the standard form, we obtain a finite value as expected by the
Kerr/CFT correspondence.
Journal of High Energy Physics 10/2010; 2010(12). DOI:10.1007/JHEP12(2010)073 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present holographic descriptions of thermalization in conformal field theories using probe D-branes in AdS X S space-times. We find that the induced metrics on Dp-brane worldvolumes which are rotating in an internal sphere direction have horizons with characteristic Hawking temperatures even if there is no black hole in the bulk AdS. The AdS/CFT correspondence applied to such systems indeed reveals thermal properties such as Brownian motions and AC conductivities in the dual conformal field theories. We also use this framework to holographically analyze time-dependent systems undergoing a quantum quench, where parameters in quantum field theories, such as a mass or a coupling constant, are suddenly changed. We confirm that this leads to thermal behavior by demonstrating the formation of apparent horizons in the induced metric after a certain time. Comment: LaTeX, 47 pages, 14 figures; Typos corrected and references added (v2); minor corrections, references added(v3)
Journal of High Energy Physics 05/2010; 2010(7). DOI:10.1007/JHEP07(2010)071 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We analyze the five-dimensional AdS gravity coupled to a gauge field and a charged scalar field. Under a Scherk-Schwarz compactification, we show that the system undergoes a superconductor/insulator transition at zero temperature in 2+1 dimensions as we change the chemical potential. By taking into account a confinement/deconfinement transition, the phase diagram turns out to have a rich structure. We will observe that it has a similarity with the RVB (resonating valence bond) approach to high-Tc superconductors via an emergent gauge symmetry. Comment: 25 pages, 23 figures; A new subsection on a concrete string theory embedding added, references added (v2); Typos corrected, references added (v3)
Journal of High Energy Physics 11/2009; 2010(3). DOI:10.1007/JHEP03(2010)131 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study possibilities of string theory embeddings of the gravity duals for non-relativistic Lifshitz-like theories with anisotropic scale invariance. We search classical solutions in type IIA and eleven-dimensional supergravities which are expected to be dual to (2+1)-dimensional Lifshitz-like theories. Under reasonable ansaetze, we prove that such gravity duals in the supergravities are not possible. We also discuss a possible physical reason behind this. Comment: 18 pages, Latex, flux conditions clarified (v2), brief summary of results added (v3)
Journal of High Energy Physics 08/2009; 2009(10). DOI:10.1088/1126-6708/2009/10/015 · 6.11 Impact Factor