Domenico Seminara

Topological strings and large N phase transitions. II. Chiral expansion of q-deformed Yang-Mills theory

We continue our study of the large N phase transition in q-deformed Yang-Mills theory on the sphere and its role in connecting topological strings to black hole entropy. We study in detail the chiral theory defined in terms of uncoupled single U(N) representations at large N and write down the resulting partition function by means of the topological vertex. The emergent toric geometry has three Kaehler parameters, one of which corresponds to the expected fibration over the sphere. By taking a suitable double-scaling limit we recover the chiral Gross-Taylor string expansion. To analyse the phase transition we construct a matrix model which describes the chiral gauge theory. It has three distinct phases, one of which should be described by the closed topological string expansion. We verify this expectation by explicit comparison between the matrix model and the chiral topological string free energies. We also show that the critical point in the pertinent phase of the matrix model corresponds to a divergence of the topological string perturbation series.

Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory

Abstract We study the relationship between instanton counting in N = 4 Yang–Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang–Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang–Mills theory and Chern–Simons theory on generic Lens spaces, and use it to show that the known instanton counting is only reproduced when the Chern–Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.

Phase transitions, double-scaling limit, and topological strings

Topological strings on Calabi–Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi–Yau threefolds given by a bundle over a two-sphere. This theory can be regarded as a q–deformation of Hurwitz theory, and it has a conjectural nonperturbative description in terms of q–deformed 2d Yang–Mills theory. We solve the planar model and find a phase transition at small radius in the universality class of 2d gravity. We give strong evidence that there is a double–scaled theory at the critical point whose all genus ∞

New supersymmetric Wilson loops in ABJ(M) theories

Abstract We present two new families of Wilson loop operators in N = 6 supersymmetric Chern–Simons theory. The first one is defined for an arbitrary contour on the three dimensional space and it resembles the Zarembo construction in N = 4 SYM. The second one involves arbitrary curves on the two dimensional sphere. In both cases one can add certain scalar and fermionic couplings to the Wilson loop so it preserves at least two supercharges. Some previously known loops, notably the 1/2 BPS circle, belong to this class, but we point out more special cases which were not known before. They could provide further tests of the gauge/gravity correspondence in the ABJ(M) case and interesting observables, exactly computable by localization techniques.

Tree Amplitudes and Two-loop Counterterms in D=11 Supergravity

We compute the tree level 4-particle bosonic scattering amplitudes in D = 11 supergravity. By construction, they are part of a linearized supersymmetry, coordinate, and 3-form gauge invariant. While this on-shell invariant is nonlocal, suitable SUSY-preserving differentiations turn it into a local one with correct dimension to provide a natural lowest (two-loop) order counterterm candidate. Its existence shows explicitly that no symmetries protect this ultimate supergravity: Indeed this invariant, together with the recently calculated infinite coefficient of its 4-graviton part, constitutes a demonstration of two-loop non-renormalizability.

Supersymmetric Wilson loops at two loops

We study the quantum properties of certain BPS Wilson loops in = 4 supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on S3 with a fraction of supersymmetry. When restricted to S2, their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM2 on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.

The generalized cusp in ABJ(M) \mathcal{N} = 6 Super Chern-Simons theories

A bstractWe construct a generalized cusped Wilson loop operator in

BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis

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