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Register a new userN=2 Supersymmetric RG Flows and the IIB Dilaton
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We show that there is a non-trivial relationship between the dilaton of IIB supergravity, and the coset of scalar fields in five-dimensional, gauged N=8 supergravity. This has important consequences for the running of the gauge coupling in massive perturbations of the AdS/CFT correspondence. We conjecture an exact analytic expression for the ten-dimensional dilaton in terms of five-dimensional quantities, and we test this conjecture. Specifically, we construct a family of solutions to IIB supergravity that preserve half of the supersymmetries, and are lifts of supersymmetric flows in five-dimensional, gauged N=8 supergravity. Via the AdS/CFT correspondence these flows correspond to softly broken N=4, large N Yang-Mills theory on part of the Coulomb branch of N=2 supersymmetric Yang-Mills. Our solutions involve non-trivial backgrounds for all the tensor gauge fields as well as for the dilaton and axion.
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We consider N=1 supersymmetric renormalization group flows of N=4 Yang-Mills theory from the perspective of ten-dimensional IIB supergravity. We explicitly construct the complete ten-dimensional lift of the flow in which exactly one chiral superfield becomes massive (the LS flow). We also examine the ten-dimensional metric and dilaton configurations for the ``super-QCD flow (the GPPZ flow) in which all chiral superfields become massive. We show that the latter flow generically gives rise to a dielectric 7-brane in the infra-red, but the solution contains a singularity that may be interpreted as a ``duality averaged ring distribution of 5-branes wrapped on S^2. At special values of the parameters the singularity simplifies to a pair of S-dual branes with (p,q) charge (1,pm 1).
We revisit the leading irrelevant deformation of $mathcal{N}=4$ Super Yang-Mills theory that preserves sixteen supercharges. We consider the deformed theory on $S^3 times mathbb{R}$. We are able to write a closed form expression of the classical action thanks to a formalism that realizes eight supercharges off shell. We then investigate integrability of the spectral problem, by studying the spin-chain Hamiltonian in planar perturbation theory. While there are some structural indications that a suitably defined deformation might preserve integrability, we are unable to settle this question by our two-loop calculation; indeed up to this order we recover the integrable Hamiltonian of undeformed $mathcal{N}=4$ SYM due to accidental symmetry enhancement. We also comment on the holographic interpretation of the theory.
We construct a continuous one parameter family of $AdS_4times S^1times S^5$ S-fold solutions of type IIB string theory which have nontrivial $SL(2,mathbb{Z})$ monodromy in the $S^1$ direction. The solutions span a subset of a conformal manifold that contains the known $mathcal{N}=4$ S-fold SCFT in $d=3$, and generically preserve $mathcal{N}=2$ supersymmetry. We also construct RG flows across dimensions, from $AdS_5times S^5$, dual to $mathcal{N}=4$, $d=4$ SYM compactified with a twisted spatial circle, to various $AdS_4times S^1times S^5$ S-fold solutions, dual to $d=3$ SCFTs. We construct additional flows between the $AdS_5$ dual of the Leigh-Strassler SCFT and an $mathcal{N}=2$ S-fold as well as RG flows between various S-folds.
We confirm the convergence of the derivative expansion in two supersymmetric models via the functional renormalization group method. Using pseudo-spectral methods, high-accuracy results for the lowest energies in supersymmetric quantum mechanics and a detailed description of the supersymmetric analogue of the Wilson-Fisher fixed point of the three-dimensional Wess-Zumino model are obtained. The superscaling relation proposed earlier, relating the relevant critical exponent to the anomalous dimension, is shown to be valid to all orders in the supercovariant derivative expansion and for all $d ge 2$.
Boundary conditions for Majorana fermions in d=1+1 dimensions fall into one of two SPT phases, associated to a mod 2 anomaly. Here we consider boundary conditions for 2N Majorana fermions that preserve a $U(1)^N$ symmetry. In general, the left-moving and right-moving fermions carry different charges under this symmetry, and implementation of the boundary condition requires new degrees of freedom, which manifest themselves in a boundary central charge, $g$. We follow the boundary RG flow induced by turning on relevant boundary operators. We identify the infra-red boundary state. In many cases, the boundary state flips SPT class, resulting in an emergent Majorana mode needed to cancel the anomaly. We show that the ratio of UV and IR boundary central charges is given by $g^2_{IR} / g^2_{UV} = {rm dim},({cal O})$, the dimension of the perturbing boundary operator. Any relevant operator necessarily has ${rm dim}({cal O}) < 1$, ensuring that the central charge decreases in accord with the g-theorem.
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