We study which bulk couplings contribute to the $S^3$ free energy $F(mathfrak{m})$ of three-dimensional ${cal N} = 2$ superconformal field theories with holographic duals, potentially deformed by boundary real-mass parameters $mathfrak{m}$. In partic
ular, we show that $F(mathfrak{m})$ is independent of a large class of bulk couplings that include non-chiral F-terms and all D-terms. On the other hand, in general, $F(mathfrak{m})$ does depend non-trivially on bulk chiral F-terms, such as prepotential interactions, and on bulk real-mass terms. These conclusions can be reached solely from properties of the AdS super-algebra, $mathfrak{osp}(2|4)$. We also consider massive vector multiplets in AdS, which in the dual field theory correspond to long single-trace superconformal multiplets of spin zero. We provide evidence that $F(mathfrak{m})$ is insensitive to the vector multiplet mass and to the interaction couplings between the massive vector multiplet and massless ones. In particular, this implies that $F(mathfrak{m})$ does not contain information about scaling dimensions or OPE coefficients of single-trace long scalar ${cal N} = 2$ superconformal multiplets.
We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the ${cal N} = 4$ $SU(N)$ super-Yang-Mills theory, in the limit where $N$ is taken to be large while the complexified Yang-Mills coupling $tau
$ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the ${cal N} = 2^*$ theory with respect to the squashing parameter $b$ and mass parameter $m$, evaluated at the values $b=1$ and $m=0$ that correspond to the ${cal N} = 4$ theory on a round sphere. At each order in the $1/N$ expansion, these fourth derivatives are modular invariant functions of $(tau, bar tau)$. We present evidence that at half-integer orders in $1/N$, these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in $1/N$, they are certain generalized Eisenstein series which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space and have interesting implications for the structure of the analogous expansion in $AdS_5times S^5$.
We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in three-dimensional $mathcal{N} = 4$ abelian gauge theories that have superconformal infrared limits. These oper
ators are position-dependent linear combinations of Coulomb branch operators. They form a one-dimensional topological sector that encodes a deformation quantization of the Coulomb branch chiral ring, and their correlation functions completely fix the ($nleq 3$)-point functions of all half-BPS Coulomb branch operators. Using these results, we provide new derivations of the conformal dimension of half-BPS monopole operators as well as new and detailed tests of mirror symmetry. Our main approach involves supersymmetric localization on a hemisphere $HS^3$ with half-BPS boundary conditions, where operator insertions within the hemisphere are represented by certain shift operators acting on the $HS^3$ wavefunction. By gluing a pair of such wavefunctions, we obtain correlators on $S^3$ with an arbitrary number of operator insertions. Finally, we show that our results can be recovered by dimensionally reducing the Schur index of 4D $mathcal{N} = 2$ theories decorated by BPS t Hooft-Wilson loops.
We construct zero-temperature solutions of supergravity theories in five and four dimensions which interpolate between two copies of anti-de Sitter space, one of which preserves an abelian gauge symmetry while the other breaks it. These domain wall s
olutions can be lifted to solutions of type IIB string theory and eleven-dimensional supergravity. They describe quantum critical behavior and emergent relativistic conformal symmetry in a superfluid or superconducting state of a strongly coupled dual gauge theory. We include computations of frequency-dependent conductivities which exhibit power law scaling in the infrared, with exponents determined by irrelevant perturbations to the symmetry-breaking anti-de Sitter background.
We use direct Kaluza-Klein reduction to calculate the spectrum of spin-2 modes around a warped product of AdS_4 and a certain squashed and stretched 7-sphere. The modes turn out to be polynomials in the four complex variables parameterizing the spher
e, and their complex conjugates. The background, which possesses U(1)_R x SU(3) symmetry, has been conjectured to be dual to a U(N) x U(N) N=2 superconformal Chern-Simons theory with a sextic superpotential. We find that the U(1)_R x SU(3) quantum numbers of spin-2 modes are in agreement with those determined in arXiv:0809.3773 through a group theoretic method, and with the spectrum of spin-2 gauge invariant operators in the Chern-Simons gauge theory. The mass-squared in AdS_4 is found to be quadratic in these quantum numbers and the Kaluza-Klein excitation number. Most of the spin-2 operators belong to long multiplets, and we determine their dimensions via the AdS/CFT correspondence.
We review methods developed in the gauge-string duality to treat energy loss by energetic probes of a strongly coupled thermal medium. After introducing the black hole description of the thermal medium, we discuss the trailing string behind a heavy q
uark and the drag force that it implies. We then explain how to solve the linearized Einstein equations in the presence of the trailing string and extract from the solutions the energy density and the Poynting vector of the dual gauge theory. We summarize some efforts to compare these calculations to heavy ion phenomenology.
We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the di
spersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Greens function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in arXiv:0708.3459.
