27 research outputs found
S-duality invariant perturbation theory improved by holography
We study anomalous dimensions of unprotected low twist operators in the
four-dimensional supersymmetric Yang-Mills theory. We
construct a class of interpolating functions to approximate the dimensions of
the leading twist operators for arbitrary gauge coupling . The
interpolating functions are consistent with previous results on the
perturbation theory, holographic computation and full S-duality. We use our
interpolating functions to test a recent conjecture by the
superconformal bootstrap that upper bounds on the dimensions are saturated at
one of the duality-invariant points and . It turns
out that our interpolating functions have maximum at , which
are close to the conjectural values by the conformal bootstrap. In terms of the
interpolating functions, we draw the image of conformal manifold in the space
of the dimensions. We find that the image is almost a line despite the
conformal manifold is two-dimensional. We also construct interpolating
functions for the subleading twist operator and study level crossing phenomenon
between the leading and subleading twist operators. Finally we study the
dimension of the Konishi operator in the planar limit. We find that our
interpolating functions match with numerical result obtained by Thermodynamic
Bethe Ansatz very well. It turns out that analytic properties of the
interpolating functions reflect an expectation on a radius of convergence of
the perturbation theory.Comment: 39+14 pages, 22 figures; v3: minor correction
Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy
We develop new techniques to efficiently evaluate heat kernel coefficients
for the Laplacian in the short-time expansion on spheres and hyperboloids with
conical singularities. We then apply these techniques to explicitly compute the
logarithmic contribution to black hole entropy from an N=4 vector multiplet
about a Z(N) orbifold of the near-horizon geometry of quarter--BPS black holes
in N=4 supergravity. We find that this vanishes, matching perfectly with the
prediction from the microstate counting. We also discuss possible
generalisations of our heat kernel results to higher-spin fields over Z(N)
orbifolds of higher-dimensional spheres and hyperboloids.Comment: 41 page
Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
We compute the logarithmic correction to black hole entropy about
exponentially suppressed saddle points of the Quantum Entropy Function
corresponding to Z(N) orbifolds of the near horizon geometry of the extremal
black hole under study. By carefully accounting for zero mode contributions we
show that the logarithmic contributions for quarter--BPS black holes in N=4
supergravity and one--eighth BPS black holes in N=8 supergravity perfectly
match with the prediction from the microstate counting. We also find that the
logarithmic contribution for half--BPS black holes in N = 2 supergravity
depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the
results we had previously obtained for heat kernel coefficients on Z(N)
orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a
generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to
an expression involving the Harish-Chandra character of SL(2,R), a result which
is of possible mathematical interest.Comment: 40 page
Second order transport from anomalies
We study parity odd transport at second order in derivative expansion for a
non-conformal charged fluid. We see that there are 27 parity odd transport
coefficients, of which 12 are non-vanishing in equilibrium. We use the
equilibrium partition function method to express 7 of these in terms of the
anomaly, shear viscosity, charge diffusivity and thermodynamic functions. The
remaining 5 are constrained by 3 relations which also involve the anomaly. We
derive Kubo formulae for 2 of the transport coefficients and show these agree
with that derived from the equilibrium partition function.Comment: Error in total number of independent parity odd transport
coefficients has been corrected from 29 to 27. Results for the relation of
the transport coefficients to the anomaly unchanged. Added a section on
chiral dispersion relations, includes additional references. Added two
appendices and corrected some typos. 34 page
Higher Spin Cosmology
We construct cosmological solutions of higher spin gravity in 2+1 dimensional
de Sitter space. We show that a consistent thermodynamics can be obtained for
their horizons by demanding appropriate holonomy conditions. This is equivalent
to demanding the integrability of the Euclidean boundary CFT partition
function, and reduces to Gibbons-Hawking thermodynamics in the spin-2 case. By
using a prescription of Maldacena, we relate the thermodynamics of these
solutions to those of higher spin black holes in AdS_3.Comment: 21 pages, v2: many typos fixed, refs added, v3: minor
corrections/improvements, Phys. Rev. D version, v4: one more re
Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
We compute logarithmic corrections to the twisted index in
four-dimensional and string theories using the
framework of the Quantum Entropy Function. We find that these vanish, matching
perfectly with the large--charge expansion of the corresponding microscopic
expressions.Comment: v2 : 22 pages, presentation significantly improved, published in JHE
Currents and Radiation from the large Black Hole Membrane
It has recently been demonstrated that black hole dynamics in a large number
of dimensions reduces to the dynamics of a codimension one membrane
propagating in flat space. In this paper we define a stress tensor and charge
current on this membrane and explicitly determine these currents at low orders
in the expansion in . We demonstrate that dynamical membrane
equations of motion derived in earlier work are simply conservation equations
for our stress tensor and charge current. Through the paper we focus on
solutions of the membrane equations which vary on a time scale of order unity.
Even though the charge current and stress tensor are not parametrically small
in such solutions, we show that the radiation sourced by the corresponding
membrane currents is generically of order . In this regime it
follows that the `near horizon' membrane degrees of freedom are decoupled from
asymptotic flat space at every perturbative order in the
expansion. We also define an entropy current on the membrane and use the
Hawking area theorem to demonstrate that the divergence of the entropy current
is point wise non negative. We view this result as a local form of the second
law of thermodynamics for membrane motion.Comment: 104 pages plus 69 pages appendix, 1 figure, Minor correction