When mass-deformed ABJM theory is considered on S 3 , the partition function of the theory localises, and is given by a matrix model. At large N , we solve this model in the decompactification limit, where the radius of the three-sphere is taken to infinity. In this limit, the theory exhibits a rich phase structure with an infinite number of third-order quantum phase transitions, accumulating at strong coupling.

The phase structure of ABJM theory with mass m deformation and nonvanishing Fayet-Iliopoulos (FI) parameter, ζ, is studied through the use of localisation on S 3 . The partition function of the theory then reduces to a matrix integral, which, in the large N limit and at large sphere radius, is exactly computed by a saddle-point approximation. When the couplings are analytically continued to real values, the phase diagram of the model becomes immensely rich, with an infinite series of third-order phase transitions at vanishing FI-parameter [1]. As the FI term is introduced, new effects appear. For any given 0 < ζ < m/2, the number of phases is finite and for ζ ≥ m/2 the theory does not have any phase transitions at all. Finally, we argue that ABJM theory with physical couplings does not undergo phase transitions and investigate the case of U(2) × U(2) gauge group in detail by an explicit calculation of the partition function.

We study the Page curve and the island rule for black holes evaporating into gravitating baths, with an eye towards establishing a connection with the ER=EPR proposal. We consider several models of two entangled 2d black holes in Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first, “doubled PSSY,” model is one in which the black holes have end-of-the-world (ETW) branes with a flavour degree of freedom. We study highly entangled states of this flavour degree of freedom and find an entanglement-induced Hawking-Page-like transition from a geometry with two disconnected black holes to one with a pair of black holes connected by a wormhole, thus realising the ER = EPR proposal. The second model is a dynamical one in which the ETW branes do not have internal degrees of freedom but the JT gravity is coupled to a 2d CFT, and we entangle the black holes by coupling the two CFTs at the AdS boundary and evolving for a long time. We study the entanglement entropy between the two black holes and find that the story is substantially similar to that with a non-gravitating thermal bath. In the third model, we couple the two ends of a two-sided eternal black hole and evolve for a long time. Finally, we discuss the possibility of a Hawking-Page-like transition induced by real-time evolution that realises the ER = EPR proposal in this dynamical setting.

We consider a twisted version of the abelian (2, 0) theory placed upon a Lorentzian six-manifold with a product structure, M 6 = C × M 4 . This is done by an investigation of the free tensor multiplet on the level of equations of motion, where the problem of its formulation in Euclidean signature is circumvented by letting the time-like direction lie in the two-manifold C and performing a topological twist along M 4 alone. A compactification on C is shown to be necessary to enable the possibility of finding a topological field theory. The hypothetical twist along a Euclidean C is argued to amount to the correct choice of linear combination of the two supercharges scalar on M 4 . This procedure is expected and conjectured to result in a topological field theory, but we arrive at the surprising conclusion that this twisted theory contains no Q-exact and covariantly conserved stress tensor unless M 4 has vanishing curvature. This is to our knowledge a phenomenon which has not been observed before in topological field theories. In the literature, the setup of the twisting used here has been suggested as the origin of the conjectured AGT-correspondence, and our hope is that this work may somehow contribute to the understanding of it.

Abstract:Herein, we consider a topologically twisted version of maximally supersymmetric Yang-Mills theory in five dimensions which was introduced by Witten in 2011. We consider this theory on a five manifold of the form M 4 × I for M 4 an oriented Riemannian four manifold. The complete and unique action of the theory in bulk is written down and is shown to be invariant under two scalar supersymmetries.arXiv:1212.5019v3 [hep-th]