Quantum Fields and Strings

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is still an open problem. We address this issue by relating the quaternionic-Kähler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions.

In this talk we discuss a proposed dual matrix formulation of N = 4 Super Yang-Mills on R^4 coupled to 4D Einstein supergravity. We review the evidence accumulated so far in favor of this proposal, which includes a successful match of the symmetries of the continuum theory, and the computation of MHV gluon and graviton scattering amplitudes in terms of matrix model correlators. We also discuss some avenues of ongoing investigation.

Three-dimensional fluids with nontrivial vorticity can be described holographically. It is well-known that the Kerr-AdS geometry gives rise to a 'cyclonic' flow. Lorentzian Taub--NUT--AdS_4 geometries give rise to a rotating fluid with vortex flow.

The boundary conditions of general black holes in asymptotically flat spacetimes can be modified such that a conformal symmetry emerges. The black holes with asymptotic geometry modified in this manner satisfy the equations of motion of minimal supergravity in one dimension more. Their symmetry suggests that a dual conformal field theory description exists that can account for the black hole entropy even in the case of black holes that are far from extremality.

We evaluate the partition function of three dimensional general relativity with a negative cosmological constant, including all known perturbative and non-perturbative contributions to the sum over geometries.

I will present a newly found duality between an infinite class of 3-dimensional N=4 gauge theories at their conformal IR fixed point and type IIB string theory solutions. This correspondence gives a new tool to explore the strongly coupled phase of the supersymmetric gauge theories in question.

We study the constraints imposed by the existence of a single higher spin conserved current on a three dimensional conformal field theory. A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of $N$ free bosons or free fermions. This is an extension of the Coleman-Mandula theorem to CFT's, which do not have a conventional S matrix. We also briefly discuss the case where the higher spin symmetries are ``slightly'' broken.

The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. In this talk I will describe a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of a Fermi gas. This new approach leads to a completely elementary derivation of the N^{3/2} behavior for ABJM theory and other quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the semiclassical expansion of the quantum gas.

In this talk I will give an overview of localization and some of its applications for QFTs in three dimensions. I will start by reviewing the localization procedure for N=2 supersymmetric gauge theories in three dimensions on S^3. I will then describe some of the applications to field theory dualities and to holography, and the possibility of extracting information about RG fixed points from the localized partition function.

We investigate the use of the embedding formalism and the Mellin transform in the calculation of tree-level conformal correlation functions in $AdS$/CFT. We evaluate 5- and 6-point Mellin amplitudes in $phi^3$ theory and even a 12-pt diagram in $phi^4$ theory, enabling us to conjecture a set of Feynman rules for scalar Mellin amplitudes. We also show how to use the same combination of Mellin transform and embedding formalism for amplitudes involving fields with spin. The complicated tensor structures which usually arise can be written as certain operators acting as projectors on much simpler index structures - essentially the same ones appearing in a flat space amplitude. Using these methods we are able to evaluate a four-point current diagram with current exchange in Yang-Mills theory.

A non-trivial test of the string vs. integrability correspondence is suggested: exact equivalence is established between strings in AdS4 x CP3 and the Gromov-Vieira all-loop integrable chain. To do that, the complete one- and two-magnon sector of each respective theory are calculated. In the single-magnon sector a direct perturbative one-loop calculation proves the validity of the dispersion law coming from the Bethe Ansatz, rather than of the one coming from the semiclassical analysis. In the two-magnon sector the full spectrum of the finite-size corrections has been calculated on the string side by us for the first time, that proves to be identical to the integrable chain spectrum. These results are interpreted by us as a confirmation of the exactness of the conjectured Gromov-Vieira Bethe Ansatz.