90 research outputs found
The gravity dual of supersymmetric gauge theories on a squashed
We present a new one-parameter family of supersymmetric solutions deforming
AdS_5. This is constructed as an asymptotically locally anti de Sitter (AlAdS)
solution of five-dimensional minimal gauged supergravity, with topology R x R^4
and a non-trivial graviphoton field, and can be uplifted to ten or eleven
dimensional supergravities. An analytic continuation of this solution yields
the gravity dual to a class of four-dimensional N=1 supersymmetric gauge
theories on a curved manifold with topology S^1 x S^3, comprising an SU(2) x
U(1)-symmetric squashed three-sphere, with a non-trivial background gauge field
coupling to the R-symmetry current. We compute the holographically renormalised
on-shell action and interpret it in terms of the Casimir energy of the dual
field theory. We also determine the holographic conserved charges of the
solution and discuss relations between them.Comment: 57 pages, 5 figures. v4: version published in JHE
Tri-Sasakian consistent reduction
We establish a universal consistent Kaluza-Klein truncation of M-theory based
on seven-dimensional tri-Sasakian structure. The four-dimensional truncated
theory is an N=4 gauged supergravity with three vector multiplets and a
non-abelian gauge group, containing the compact factor SO(3). Consistency
follows from the fact that our truncation takes exactly the same form as a
left-invariant reduction on a specific coset manifold, and we show that the
same holds for the various universal consistent truncations recently put
forward in the literature. We describe how the global symmetry group SL(2,R) x
SO(6,3) is embedded in the symmetry group E7(7) of maximally supersymmetric
reductions, and make the connection with the approach of Exceptional
Generalized Geometry. Vacuum AdS4 solutions spontaneously break the amount of
supersymmetry from N=4 to N=3,1 or 0, and the spectrum contains massive modes.
We find a subtruncation to minimal N=3 gauged supergravity as well as an N=1
subtruncation to the SO(3)-invariant sector. We also show that a reduction on
the homogeneous space N^{010} enhances the universal tri-Sasakian truncation
with a Betti vector multiplet.Comment: 40 pages main text, 9 pages appendix, 1 figure, 6 tables, v2: JHEP
version, added references, minor corrections, changed notation fluctuations
in tables 2-
BPS domain walls in N=4 supergravity and dual flows
We establish the conditions for supersymmetric domain wall solutions to N=4
gauged supergravity in five dimensions. These read as BPS first-order equations
for the warp factor and the scalar fields, driven by a superpotential and
supplemented by a set of constraints that we specify in detail. Then we apply
our results to certain consistent truncations of IIB supergravity, thus
exploring their dual field theory renormalization group flows. We find a
universal flow deforming superconformal theories on D3-branes at Calabi-Yau
cones. Moreover, we obtain a superpotential for the solution corresponding to
the baryonic branch of the Klebanov-Strassler theory, as well as the
superpotential for the flow describing D3 and wrapped D5-branes on the resolved
conifold.Comment: 42 pages, 1 figure. v2: minor changes, matches published versio
Localization on Hopf surfaces
We discuss localization of the path integral for supersymmetric gauge
theories with an R-symmetry on Hermitian four-manifolds. After presenting the
localization locus equations for the general case, we focus on backgrounds with
S^1 x S^3 topology, admitting two supercharges of opposite R-charge. These are
Hopf surfaces, with two complex structure moduli p,q. We compute the localized
partition function on such Hopf surfaces, allowing for a very large class of
Hermitian metrics, and prove that this is proportional to the supersymmetric
index with fugacities p,q. Using zeta function regularisation, we determine the
exact proportionality factor, finding that it depends only on p,q, and on the
anomaly coefficients a, c of the field theory. This may be interpreted as a
supersymmetric Casimir energy, and provides the leading order contribution to
the partition function in a large N expansion.Comment: v2: discussion of background reality conditions modified and other
minor changes, references added; v3: further minor corrections, version
accepted for publication in JHE
The BPS limit of rotating AdS black hole thermodynamics
We consider rotating, electrically charged, supersymmetric AdS black holes in
four, five, six and seven dimensions, and provide a derivation of the
respective extremization principles stating that the Bekenstein-Hawking entropy
is the Legendre transform of a homogeneous function of chemical potentials,
subject to a complex constraint. Extending a recently proposed BPS limit, we
start from finite temperature and reach extremality following a supersymmetric
trajectory in the space of complexified solutions. We show that the entropy
function is the supergravity on-shell action in this limit. Chemical potentials
satisfying the extremization equations also emerge from the complexified
solution.Comment: 51 pages; v3: new appendix on Legendre transform of the general
entropy function (6.1), matches published versio
Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS black holes
We present a holographic derivation of the entropy of supersymmetric
asymptotically AdS black holes. We define a BPS limit of black hole
thermodynamics by first focussing on a supersymmetric family of complexified
solutions and then reaching extremality. We show that in this limit the black
hole entropy is the Legendre transform of the on-shell gravitational action
with respect to three chemical potentials subject to a constraint. This
constraint follows from supersymmetry and regularity in the Euclidean bulk
geometry. Further, we calculate, using localization, the exact partition
function of the dual SCFT on a twisted with
complexified chemical potentials obeying this constraint. This defines a
generalization of the supersymmetric Casimir energy, whose Legendre transform
at large exactly reproduces the Bekenstein-Hawking entropy of the black
hole.Comment: v4: minor changes, version published in JHE
The large- limit of the 4d superconformal index
We systematically analyze the large- limit of the superconformal index of
superconformal theories having a quiver description. The index
of these theories is known in terms of unitary matrix integrals, which we
calculate using the recently-developed technique of elliptic extension. This
technique allows us to easily evaluate the integral as a sum over saddle points
of an effective action in the limit where the rank of the gauge group is
infinite. For a generic quiver theory under consideration, we find a special
family of saddles whose effective action takes a universal form controlled by
the anomaly coefficients of the theory. This family includes the known
supersymmetric black hole solution in the holographically dual AdS
theories. We then analyze the index refined by turning on flavor chemical
potentials. We show that, for a certain range of chemical potentials, the
effective action again takes a universal cubic form that is controlled by the
anomaly coefficients of the theory. Finally, we present a large class of
solutions to the saddle-point equations which are labelled by group
homomorphisms of finite abelian groups of order into the torus.Comment: 58 pages; v2: minor changes, published versio
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