Abstract:

In order to study the weakly coupled regime of theory we often make use of perturbative expansion of the physical quantities of interest. But such expansions are often divergent and defined only as asymptotic series. In fact, this divergence is connected to the existence of non-perturbative contributions, i.e. instanton effects that cannot be captured by a perturbative analysis. The theory of resurgence is a mathematical tool which allows us to effectively study this connection and its consequences. In this talk we will make use of this theory in order to show how to construct a full non-perturbative solution from perturbative data. To write this full non-perturbative solution we need to introduce generalised multi-instanton sectors, which can then be checked by precision tests on the asymptotic data. Finally, the study of this non-perturbative sectors in matrix models allows us to have a full picture of the phase diagram of this models.

Abstract:

The Wilson loop is one of the most important observables in gauge theories. It has long been suspected that its dynamics should have a natural description in terms of strings. The AdS/CFT correspondence is a realisation of this idea: the expectation value of Wilson loops in maximally supersymmetric Yang-Mills theory (MSYM) in four dimensions is captured by the partition function of type IIB superstring theory on AdS₅ x S⁵, satisfying suitable boundary conditions. Accordingly, the MSYM computation at strong coupling is equivalent to a semiclassical approximation on the string theory side, and amounts to finding certain minimal area surfaces in AdS₅ x S⁵.

In this talk, we deal with the correlator of two (supersymmetric) Wilson loops with contours lying on Hopf fibers of S³. A connected classical string surface, linking two different fibers, is presented. This string theory solution describes oppositely oriented fibers, and it is able to interpolate between a supersymmetric and non-supersymmetric configuration according to the fiber position on the Hopf base. We show that the system can be thought of as a deformation of the ordinary anti-parallel lines describing the static quark-antiquark potential, which is indeed correctly reproduced, at weak and strong coupling, as the fibers approach one another.

Abstract:

In the context of gauge/string theory correspondences, the geometry of membranes and space-times must be seen as an emergent phenomenon arising from a strongly coupled quantum field theory with a large local symmetry or gauge group.

I shall discuss the dual description of membranes in terms of long, gauge-invariant, local operators in the Maldacena and ABJM correspondences, focusing primarily on a class of D-branes known as giant gravitons. These restricted Schur polynomial operators in the MSYM and ABJM theories form complete, exactly orthonormal bases with respect to the free field, two-point correlation functions and are built using the representation theory of the permutation group.

Various BPS, non-spherical, D3-brane and D4-brane giant graviton configurations, embedded into and moving on the compact spaces S⁵ and CP³, will be constructed in type IIB string theory on AdS₅xS⁵ and type IIA string theory on AdS₄xCP³ respectively. In the latter case, the D4-brane giants embedded into the complex projective space CP³ are descendants of M5-brane giant gravitons in S⁷ under the compactification on the S¹ Hopf fibre which takes S⁷ to CP³.

I shall finally discuss to what extent it has so far proven possible to view the non- trivial geometry of these membranes from the perspective of the dual operators.

Abstract:

Motivated by an attempt to formulate (non chiral) conformal field theories of principal chiral models on manifolds of supergroups with vanishing Killing form as an OPE current algebras, we consider a related class of non semisimple affine (and non affine) (super)algebras, their representation theory and construct from them a chiral CFT. We address the questions of their representations, characters, fusion rules, and modular properties.

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Abstract:

I will discuss some recent developments and applications on the duality between gauge fields and strings.

Abstract:

3d N=4 superconformal quiver theories arise as the low energy description of intersecting D3/D5/NS5 branes. I will discuss the backreacted solutions describing the near horizon of such configurations. The CFT partition function can be computed using localization technqiues and matched to the supergravity results.

Abstract:

An interesting instance of the AdS/CFT correspondence is the case of AdS3/CFT2. Strings on AdS_3xS^3xS^3xS^1 can be completely understood when the background is purely NSNS thanks to 2-dimensional conformal symmetry. Unfortunately this symmetry is not as useful in the case of RR backgrounds. However, it appears that the integrability techniques that proved successful in understanding the planar limit of AdS5/CFT4 may be applicable also here, which sparked new interest and efforts in this field.

I will review such techniques and report on some recent developments (arXiv:1211.5119, 1212.0505) in the understanding of the string spectrum on AdS_3xS^3xS^3xS^1, exploring in particular the limit in which one S^3 blows up to a flat space.