Past String Theory Seminar

The partition function of 3d N=2 superconformal theories on the

3-sphere can be computed exactly by localization methods. I will explain

some sublteties associated to that important result. As a by-product, this

analysis establishes the so-called F-maximization principle for N=2 SCFTs in

3d: the exact superconformal R-charge maximizes the 3-sphere free energy

F=-log Z.

The AdS/CFT correspondence is a powerful tool to analyse strongly coupled quantum field

theories. Over the past few years there has been a surge of activity aimed at finding

possible applications to condensed matter systems. One focus has been to holographically

realise various kinds of phases via the construction of fascinating new classes of black

hole solutions. In this framework, I will discuss the possibility of describing finite

temperature phase transitions leading to spontaneous breaking of translational invariance of

the dual field theory at strong coupling. Along with the general setup I will also discuss

specific string/M theory embeddings of the corresponding symmetry breaking modes leading to

the description of such phases.

In this talk we will review M-theory dualities and recent attempts to make these dualities manifest in eleven-dimensional supergravity. We will review the work of Berman and Perry and then outline a prescription, called non-linear realisation, for making larger duality symmetries manifest. Finally, we will explain how the local symmetries are described by generalised geometry, which leads to a duality-covariant constraint that allows one to reduce from generalised space to physical space.

The moduli space of supersymmetric (eighth-BPS) giant gravitons in $AdS_5 \times S^5$ is a limit of projective spaces. Quantizing this moduli space produces a Fock space of oscillator states, with a cutoff $N$ related to the rank of the dual $U(N)$ gauge group. Fuzzy geometry provides the ideal set of techniques for associating points or regions of moduli space to specific oscillator states. It leads to predictions for the spectrum of BPS excitations of specific worldvolume geometries. It also leads to a group theoretic basis for these states, containing Young diagram labels for $U(N)$ as well as the global $U(3)$ symmetry group. The problem of constructing gauge theory operators corresponding to the oscillator states and  some recent progress in this direction are explained.

I will describe the recent construction of new supersymmetric compactifications of the heterotic string which yield just the spectrum of the MSSM at low energies. The starting point is the standard embedding solution on a Calabi-Yau manifold with Euler number -6 with various choices of Wilson lines, i.e., various choices of discrete holonomy for the gauge bundle. Although they yield three net generations of standard model matter, such models necessarily have a larger gauge group than the standard model, as well as exotic matter content. Families of stable bundles can be obtained by deformation of these simple solutions, the deformation playing the dual role of partially breaking the gauge group and reducing the matter content, and in this way we construct more realistic models. The moduli space breaks up into various branches depending on the initial choice of Wilson lines, and on eight of these branches we find models with exactly the standard model gauge group, three generations of quarks and leptons, two Higgs doublets, and no other massless charged states. I will also comment on why these are possibly the unique models of this type.

We study pure Seiberg-Witten theories with $SU(r+1)$ and $Sp(2r)$ gauge groups with no flavors. We study singularity loci of moduli space of the Seiberg-Witten curve. Using exterior derivative and discriminant operators, we can find Argyres-Douglas loci of the SW theory. We also compute BPS charges of the massless dyons of $SU$ and $Sp$ SW theory. In a detailed example of $C_2=Sp(4)$, we find 6 points in the moduli space where we have 2 massless BPS dyons, and 3 of them give Argyres-Douglas loci. We show that BPS charges of the massless dyons jump as we go across Argyres-Douglas loci, giving an explicit example of Argyres-Douglas loci living inside the wall of marginal stability. (Based on work in progress with Keshav Dasgupta)

I shall describe the construction of the four-brane giant graviton on $\mathrm{AdS}_4\times \mathbb{CP}^3$ (extended and moving in the complex projective space), which is dual to a subdeterminant operator in the ABJM model. This dynamically stable, BPS configuration factorizes at maximum size into two topologically stable four-branes (each wrapped on a different $\mathbb{CP}^2 \subset \mathbb{CP}^3$ cycle) dual to ABJM dibaryons. Our study of the spectrum of small fluctuations around this four-brane giant provides good evidence for a dependence in the spectrum on the size, $\alpha_0$, which is a direct result of the changing shape of the giant’s worldvolume as it grows in size. I shall finally comment upon the implications for operators in the non-BPS, holomorphic sector of the ABJM model.

I will present a two-parameter family of Wilson loop operators in N = 4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. These loops are calculated on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. I will comment about the feasibility of deriving all-loop results for these Wilson loops.

I will discuss the dynamical emergence of IR conformal invariance describing the low energy excitations of near-extremal R-charged global AdS${}_5$ black holes. To keep some non-trivial dynamics in the sector of ${\cal N}=4$ SYM captured by the near horizon limits describing these IR physics, we are lead to study large N limits in the UV theory involving near vanishing horizon black holes. I will consider both near-BPS and non-BPS regimes, emphasising the differences in the local AdS${}_3$ throats emerging in both cases. I will compare these results with the predictions obtained by Kerr/CFT, obtaining a natural quantisation for the central charge of the near-BPS emergent IR CFT describing the open strings stretched between giant gravitons.

In just the last year it has been realized that one can define supersymmetric gauge theories on non-trivial compact curved manifolds, coupled to a background R-symmetry gauge field, and moreover that expectation values of certain BPS operators reduce to finite matrix integrals via a form of localization. I will argue that a general approach to this topic is provided by the gauge/gravity correspondence. In particular, I will present several examples of supersymmetric gauge theories on different 1-parameter deformations of the three-sphere, which have a large N limit, together with their gravity duals (which are solutions to Einstein-Maxwell theory). The Euclidean gravitational partition function precisely matches a large N matrix model evaluation of the field theory partition function, as an exact \emph{function} of the deformation parameter.

I will study the sequestering of blow-up fields through a CFT in a toroidal orbifold setting. In particular, I will examine the disk correlator between orbifold blow-up moduli and matter Yukawa couplings. Blow-up moduli appear as twist fields on the worldsheet which introduce a monodromy

condition for the coordinate field X. Thus I will focus on how the presence of twist field affects

the CFT calculation of disk correlators. Further, I will explain how the results are relevant to

suppressing soft terms to scales parametrically below the gravitino mass. Last, I want to explore the

relevance of our calculation for the case of smooth Calabi-Yaus.

Consistent truncations have proved to be powerful tools in the construction of new string theory solutions. Recently, they have been employed in the holographic description of condensed matter systems. In the talk, I will present a rich class of supersymmetric consistent truncations of higher-dimensional supergravity which are based on geometric structures, focusing on the tri-Sasakian case. Then I will discuss some applications, including a general result relating AdS backgrounds to solutions with non-relativistic Lifshitz symmetry.

We compute three-point functions of single trace operators in planar N = 4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.

String compactifications incorporating non-vanishing H-flux have received increased attention over the past decade for their potential relevance to the moduli stabilization problem. Their internal spaces are in general not Kähler and, therefore, not Calabi-Yau. In the heterotic string an important technical problem is to construct gauge bundles on such spaces. I will present a method of how to explicitly construct gauge bundles over homogeneous nearly-Kähler manifolds of dimension six and discuss some of the arising implications for model building.

Four-dimensional (4d) supergravities with non-geometric terms in their potential are very promising models for phenomenology. Indeed, these terms, generated by so-called non-geometric fluxes, generically help to obtain de Sitter vacua, or to stabilise moduli. Unfortunately, deriving these theories from a compactified ten-dimensional (10d) supergravity has not been achieved so far. One reason is that non-geometric fluxes do not seem to match any 10d field, and another reason is the appearance of global issues in 10d non-geometric configurations.

After reviewing some background material, we present in this talk a solution to the two previous issues. Thanks to a field redefinition, we make the non-geometric Q-flux appear in a 10d action, which only differs from the NSNS action by a total derivative. In addition, this new action is globally well-defined, at least in some examples, and one can then perform the dimensional reduction to recover the 4d non-geometric potential. We also mention an application to the heterotic string.

Based on 1106.4015.

The study of superconformal Chern-Simons theories has led to a deeper understanding of M-theory and a new example of the AdS/CFT correspondence. In this talk, I will give an overview of superconformal Chern-Simons theories and their gravity duals. I will also describe some recent work on scattering amplitudes in these theories.

Recently, two new Calabi-Yau threefolds have been discovered which have small Hodge numbers, and give rise to three chiral generations of fermions via the so-called 'standard embedding' compactification of the heterotic string.
In this talk I will describe how to deform the standard embedding on these manifolds in order to achieve the correct gauge group.  I will also describe how to calculate the resulting spectrum and interactions, which is still work in progress.