Kavli IPMU Workshop on Gauge and String Theory

26 Aug 2013, 15:00 → 6 Sept 2013, 17:00 Asia/Tokyo

Lecture hall (Kavli IPMU)

Monday 26 August

15:00 teatime

Tuesday 27 August

15:00 teatime

1 Length Changing Supersymmetry in Integrable Spin Chains

We investigate the integrable gl(m|n) nearest-neighbor spin chains in the rational and trigonometric case and identify the allowed representations and values of the deformation parameter q for which there exist length-changing symmetry generators that commute with the transfer matrix.

Speaker: Dr Vladimir Mitev (Humboldt University of Berlin)

2 Superconformal field theory and supersymmetric sine-Gordon model with Dirichlet boundary conditions

The supersymmetric sine-Gordon model is known as a perturbation from the N=1 c=3/2 superconformal field theory. The connection between these two theories has been studied by taking the ultraviolet limit of the supersymmetric sine-Gordon model. The N=1 superconformal field theory is the theory of a free Majorana fermion and a free boson, whose Hilbert space therefore consists of a tensor product of the fermionic part and the bosonic part. There exist three independent sectors in the fermionic part, each of which is obtained as a descendant of three different primary fields characterized by different conformal weights h=1, 1/2, and 1/16. The sectors of h=1 and h=1/2 can be combined into one superconformal sector named the Neveu-Schwarz sector. The h=1/16 sector is called the Ramond sector. The supersymmetric sine-Gordon model is also obtained from a scaling limit of the spin-1 XXZ model with alternating inhomogeneity. Although it has been pointed out that only the h=1 Neveu-Schwarz sector of the supersymmetric sine-Gordon model can be realized from the spin chain under the periodic boundary condition, we found that imposing the Dirichlet boundary conditions on both ends and computing the conformal dimension through the ultraviolet limit let us obtain the other sectors with the proper choice of boundary parameters. In the context of the corresponding spin chain, the phase transition between the Neveu-Schwarz sector and the Ramond sector is obtained in a plot of magnetic fields with respect to a boundary parameter as the separation into two sectors with different periodicity.

Speaker: Dr Chihiro Matsui (University of Tokyo)

Wednesday 28 August

15:00 teatime

3 Schroedinger Sigma Models and Jordanian Twists

We consider the classical integrable structure of two-dimensional non-linear sigma models defined on 3D Schrodinger spacetime (called the Schrodinger sigma models). The global symmetry is SL(2)_L x U(1)_R. The SL(2)_L symmetry is enhanced to the Yangian Y(sl(2)). We show that the U(1)_R symmetry is enhanced to a Jordanian twisted Yangian. Finally I will discuss the Landau-Lifshitz limit if I have time.

Speaker: Dr Kentaroh Yoshida (Kyoto University)

4 Massive world-sheet S-matrices of integrable string theories

Recently there has been substantial progress in the study of world-sheet S-matrices describing the scattering of massive modes in various (BMN light-cone gauge-fixed and decompactified) AdS_3 x S³ x M⁴ string theories via both perturbation theory and integrability. In this talk I will outline these developments, present some preliminary results for AdS_2 x S² x T⁶, and attempt to put them into context through comparisons with the well-known case of AdS_5 x S⁵.

Speaker: Dr Ben Hoare (Humboldt-Universität zu Berlin)

Thursday 29 August

15:00 teatime

5 MHV amplitude around regular polygonal limit

We discuss the MHV amplitude/null-polygonal Wilson loop of $ {¥cal N} =4 $ SYM at strong coupling. The amplitude/Wilson loop is evaluated by the area of minimal surfaces in AdS, which are analyzed by integral equations of the thermodynamic Bethe ansatz (TBA) type. When the surfaces are embedded in AdS$_{3}$ or AdS$_{4}$, the integral equations are identified with the usual TBA equations of a two-dimensional integrable model called homogeneous sine-Gordon (HSG) model. The HSG model is obtained by an integrable deformation of a coset CFT. In special cases, the associated TBA system reduces to simpler ones for perturbed diagonal coset CFTs/(W-)minimal models. Based on these facts, we derive an analytic expansion of the amplitude/Wilson loop around the limit where the Wilson loop becomes regular polygonal.

Speaker: Dr Yuji Satoh (University of Tsukuba)

6 Two-Loop Unitarity

The unitarity method is a key part of the set of on-shell methods for calculating gauge-theory amplitudes both analytically and numerically. These methods have been used successfully to obtain the one-loop amplitudes needed for a variety of cutting-edge high-multiplicity next-to-leading order calculations for LHC physics. In this talk, I present the first steps in extending maximal unitarity to a computation of two-loop amplitudes, needed for precision LHC calculations. I present the formalism for double-box integrals with various external masses, and aspects of the extension to slashed-box integrals.

Speaker: Dr David Kosower (IPhT, CEA-Saclay)

Friday 30 August

15:00 teatime

7 On three point functions in SU(2)-sector at strong coupling

I will talk about my ongoing (almost finished) project about correlation functions of three non-BPS heavy operators in the SU(2)-sector in N=4 SYM at strong coupling. The computation is done by evaluating the area and the contributions of the vertex operators of the string worldsheet in AdS_3 \times S^3 using integrability. I will describe the basic idea and an outline of our method, and show partial results. If time permits, I will also mention the application of our method to the classical limit of DOZZ 3-pnt functions in Liouville theory.

Speaker: Mr Shota Komatsu (University of Tokyo)

8 On the three-point functions of heavy fields in the SU(2) sector of N=4 SYM

We present some exact results about the tree-level 3-point function of local single-trace operators in the scalar sector of planar N = 4 supersymmetric Yang-Mills. Explicit expressions are obtained for particular cases involving su(2) and su(3) type fields, where the 3pt function can be written as a determinant. In the limit of large conformal weights of the operators, the 3pt function depends in a universal way of the three quasimomenta and the way they split into a left and right piece.

Speaker: Dr Ivan Kostov (IPhT - Saclay)

Monday 2 September

9 Line operators and dualities of 4d gauge theories

Speaker: Dr Yuji Tachikawa (University of Tokyo)

15:00 teatime

Tuesday 3 September

10 Exact results in two-dimensional (2,2) supersymmetric gauge theories with boundary

Speaker: Kentaro Hori and Mauricio Romo

12:00 Photo shoot

15:00 teatime

18:00 Reception

Wednesday 4 September

11 The Superconformal Bootstrap -- Overview and Exact Results

Speaker: Prof. Leonardo Rastelli (YITP, Stony Brook Univeristy)

15:00 teatime

Thursday 5 September

12 Integrability as Gauge-Theory Duality

Speaker: Dr Masahito Yamazaki (IAS/Kavli IPMU)

13 Yangian Symmetry of smooth Wilson Loops in N=4 SYM

Speaker: Prof. Jan PLEFKA

15:00 teatime

Friday 6 September

14 The Superconformal Bootstrap -- Results for Non-Protected Quantities

Speaker: Chris Beem and Balt van Rees

15:00 teatime