Holography and Dualities 2016: New Advances in String and Gauge Theory

30 Mar 2016, 09:00 → 22 Apr 2016, 18:00 Europe/Stockholm

122:026 (Nordita, Stockholm)

Bogdan Stefanski (City University, London), Charlotte Kristjansen (Niels Bohr Institute), Konstantin Zarembo (Nordita), Olof Ohlsson Sax (Nordita), Sergei Gukov (Caltech)

The holographic duality has provided new insights into the physics of strongly-coupled systems by bridging together different subjects thought before to be completely unrelated, such as hydrodynamics and physics of black holes, string theory and strongly-coupled phenomena in condensed-matter physics, integrable systems and non-perturbative behavior of gauge fields. Symmetries have played an important role in these developments and have led to development of new non-perturbative methods based for example on integrability, bootstrap and localization.

The aim of the program is to discuss new developments in dualities and holography, with focus on

• Gauge/string dualities
• Integrability
• Symmetries in string theory
• Supersymmetric localization
• Bootstrap methods
• Applications of holography in QCD and condensed-matter systems

Participants will include L.F. Alday (Oxford U.), M. Cederwall (Chalmers, Gothenburg), G. Festuccia (Uppsala U.), T. Harmark (NBI, Copenhagen), C. Hull (Imperial College, London), N. Gromov (King's College, London), V. Kazakov (ENS, Paris), D. Martelli (King's College, London), J. Minahan (Uppsala U.), B. Nilsson (Chalmers, Gothenburg), N. Obers (NBI, Copenhagen), J. Plefka (Humboldt U., Berlin), R. Roiban (Penn State), G. Semenoff (UBC, Vancouver), B. Sundborg (Stockholm U.), R. Szabo (Heriot-Watt U. Edinburgh), A. Tseytlin (Imperial College, London), M. Zabzine (Uppsala U.).

The program is jointly organized by Nordita, by the Marie Curie Initial Training Network GATIS, and by the COST Action MP1210 “The String Theory Universe”.

Application deadline: 12 January 2016

Thursday 31 March

1 Butterflies and constraints on holography (NORDITA SEMINAR)

I will discuss some recent attempts to formulate necessary conditions for holography based on entanglement, scrambling and the butterfly effect.

Speaker: Pawel Caputa (Nordita)

Friday 1 April

2 Analytic anisotropic solution for holography

An exact solution to Einstein's equations for holographic models is presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution's appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined in detail. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimension reduction.

Speaker: Jie Ren (Hebrew University)

3 Introduction to the program (NORDITA SEMINAR): N=4 SYM as a theorist's Valhalla

Maximally supersymmetric Yang-Mills theory in 4 dimensions (N=4 SYM) is a remarkable theory that can be studied in a variety of ways beyond traditional perturbation theory. On our quest to calculate the quark-antiquark potential in this theory we will be led by three valkyries: Holography, Integrability and Localization. They pull us in three different directions, towards string theory, matrix models and spin chains, but together enable us to calculate some quantities exactly and others to very high precision.

Speaker: Nadav Drukker (King's College)

Monday 4 April

4 Analytic bootstrap program

We will use basic properties of conformal field theories, such as symmetries and the structure of the operator product expansion, to get analytic results for the scaling dimensions of higher spin operators.

Speaker: Fernando Alday (Oxford)

5 Perturbative worldsheet calculations in AdS_2 and AdS_3

I will describe perturbative worldsheet calculations for strings in AdS_d x S^d x T^{10-2d} for d=2,3. These include the one-loop BMN S-matrix and the two-loop correction to the dispersion relation. I will discuss the subtle regularization issues that arise and the comparison to conjectured exact expressions when those are available.

Speaker: Linus Wulff (Imperial College)

17:30 Reception

Tuesday 5 April

6 Supersymmetric 5D gauge theories on toric manifolds

I will review the localization calculation for 5D supersymmetric gauge theories on the toric Sasaki-Einstein manifold. I will explain briefly how the answer is written in terms of toric data. The factorisation properties of the answer will be discussed and the relation to Nekrasov’s partition function will be explained. At the end I will discuss the modular properties of the partition function for the abelian example. If time allows I will make some comments on 6D and 7D calculations.

Speaker: Maxim Zabzine (Uppsala)

7 Demystifying the Holographic Mystique

In spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has so far been rather slow. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, despite a flurry of recent applications of the broadly defined holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains anything but firmly established. This discussion aims at ascertaining its true status and elucidating the conditions under which its predictions may indeed be right (albeit, possibly, for a wrong reason).

Speaker: Dmitri Khveshchenko (North Carolina)

Wednesday 6 April

8 Anomalous dimension of giant gravitons from non-abelian DBI and Spin Matrix theory

In this talk we begin by introducing Spin Matrix theory (SMT). It can be seen as a finite-N generalization of a nearest neighbor spin chain. SMT describes N=4 SYM near certain unitarity bounds and zero-temperature critical points. We find a new tractable regime at finite N described by a classical matrix model. Next we go to the string side of the AdS/CFT correspondence and explain that the dual is given by highly excited giant gravitons. Finally, we match the matrix model to interacting giant gravitons on AdS using the non-abelian DBI action.

Speaker: Troels Harmark (NBI)

9 Confronting exact results from localization and holography

Speaker: Dario Martelli (King's College)

Thursday 7 April

10 Smooth Wilson loops in N=4 Superspace and Yangian Symmetry

We will review the construction of smooth Maldacena-Wilson super Loops in non-chiral on-shell N=4 superspace and discuss its superconformal and Yangian symmetries.

Speaker: Jan Plefka (Humboldt)

11 Double Field Theory: an Overview

Speaker: Chris Hull (Imperial College)

Friday 8 April

12 Poles in three-point functions

Speaker: Joe Minahan (Uppsala)

13 One-point functions in AdS/dCFT

In this talk I will discuss one-point functions in the defect conformal field theory dual to a D3-D5 brane system with k units of world volume flux. In such a set-up scalar operators pick up a non-trivial vacuum expectation value. I will discuss how one can use integrability to compute these one-point functions for unprotected operators by expressing them as overlaps between Bethe eigenstates and a matrix product state. I will present a closed expression of determinant form for these one-point functions valid for any value of k. In particular, by using the transfer matrix of the Heisenberg spin chain, one can recursively relate the matrix product state for higher even and odd k to the matrix product state for k = 2 and k = 3. Furthermore, there is evidence that the matrix product states for k = 2 and k = 3 are related via a ratio of Baxter’s Q-operators.

Speaker: Marius de Leeuw (NBI)

19:00 Program Dinner

Monday 11 April

14 Deformations of AdS backgrounds: an overview

After recalling the beta- and gamma deformations, we review briefly from a worldsheet perspective the lambda deformation and the general Yang-Baxter-type deformations. Focusing on the eta deformation, we discuss its worldsheet and target space properties. While this sigma model does not appear to define a critical string theory in the usual sense; we review the modified IIB equations of motion that the corresponding field configuration satisfies and their possible relation to the worldsheet theory.

Speaker: Radu Roiban (Penn State)

15 The N=2 superconformal bootstrap

In this talk we will present an overview of the N=2 superconformal bootstrap program. We will introduce a protected subsector present in any 4d N=2 SCFT whose correlation functions are captured by a two-dimensional chiral algebra. Thanks to a subtle interplay between 4d and 2d quantities, it is possible to obtain analytic constraints that severely reduce the space of theories. Once an overall picture of the landscape is obtained, one can then use modern numerical techniques and attempt to solve individual theories numerically.

Speaker: Pedro Liendo (Humboldt)

17:30 Reception

Tuesday 12 April

16 Overview of higher-spin holography

Speaker: Soo-Jong Rey (Seoul National University)

Wednesday 13 April

17 Holographic 2+1D Weyl Semimetals

Speaker: Gordon Semenoff (UBC)

18 Quark-anti-quark potential in N=4 SYM

We construct a closed system of equations describing the quark--anti-quark potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of asymptotics. A pedagogical introduction to the Quantum Spectral Curve method will be given. We also discuss how this method can be used at weak coupling and numerically for any coupling with extremely high precision. based on 1601.05679 and 1510.02098

Speaker: Nikolay Gromov (King's College)

Thursday 14 April

19 N=2 gauge theories and geometric representation theory

Speaker: Richard Szabo (Heriot-Watt)

20 AdS3/CFT2 and integrability

Speaker: Riccardo Borsato (Imperial College)

Friday 15 April

21 Lattice N=4 Super-Yang-Mills and S-duality

Formulations of lattice supersymmetry over the last decade have been able to significantly reduce the amount of fine-tuning necessary in order to obtain the correct continuum limit. In the case of N=4 super-Yang-Mills, the approach that has emerged as the best path forward is based on a topological twisting of the theory. We describe this lattice theory and the various studies we have performed in order to understand its renormalization. A discrete subgroup of the R-symmetry has been used to identify the supersymmetric continuum limit, and we have performed nonpertubative numerical tests of it. In terms of applications, Montonen and Olive found evidence that a duality could exist in Yang-Mills with adjoint scalars. In this scheme, the 't Hooft-Polyakov monopole is dual to the W boson, leading to a theory equivalent to the Georgi-Glashow model but with magnetic charge replacing electric charge. The duality is believed to be realized in N=4 super-Yang-Mills. We are pursuing numerical, nonperturbative evidence for this S-duality using our lattice formulation. The various tricks that are necessary for doing this will be described.

Speaker: Joel Giedt (Rensselaer Polytechnic Institute)

19:00 Program Dinner

Monday 18 April

22 AdS/CFT and Higher spin scattering in flat space

Speaker: Arkady Tseytlin (Imperial College)

23 Non-relativistic conformal bootstrap

Speaker: Piotr Surowka (MPI, Munich)

17:30 Reception

Tuesday 19 April

24 Non-relativistic geometry in non-AdS holographic dualities

Newton-Cartan geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. I recent years, this geometry (including a novel generalisation that includes torsion) has made its appearance in holography for systems with non-relativistic symmetry and been studied in parallel directly in a non-relativistic field theory context. I will give an introduction to Newton-Cartan (NC) geometry and its torsional version (TNC), and show how this appears as a boundary geometry in the context of holography for bulk Lifshitz spacetimes. The coupling of field theories to TNC geometry will be discussed and I will exhibit how dynamical NC geometry leads to a covariant formulation of the known versions of Horava-Lifshitz gravity. The latter may also be used as bulk theories in a holographic context, which will be illustrated via a novel formulation of 3D Horava- Lifsthiz gravity, providing a new way to implement a non- relativistic gravity/field theory correspondence. Finally, I will outline a connection with flat space holography, which features Carollian geometry on the boundary. To conclude, I will summarize some open problems and mention progress in related directions.

Speaker: Niels Obers (NBI)

25 Scaling Laws in Quantum Quench : Holography and Field Theory

Speaker: Sumit Das (Kentucky)

Wednesday 20 April

26 Diagrams and Algebras as Holograms

Speaker: Sanjaye Ramgoolam (Queen Mary)

27 Flat space quark-antiquark potential from the Quantum Spectral Curve

We apply the integrability-based Quantum Spectral Curve framework to study the exact quark-antiquark potential in planar N=4 supersymmetric Yang-Mills theory. We focus on the singular limit corresponding to the flat space potential. We present weak coupling results to 7 loops and a numerical solution in a wide range of the coupling. We also show that in a special limit the QSC reduces to a Schrodinger equation resumming ladder diagrams to all perturbative orders.

Speaker: Fedor Levkovich-Maslyuk (King's College)

Thursday 21 April

28 Twisting new integrable QFT's out of N=4 SYM

Speaker: Vladimir Kazakov (ENS)