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String Theory Journal Club

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Zapraszamy do sali 5.42, ul. Pasteura 5 o godzinie 13:00

(IST Lisbon)

(Colored) HOMFLY-PT homology and differentials

I will give an overview of the structural properties of the HOMFLY-PT homologies and the rich set of differentials that exists on them.

Zapraszamy do sali 5.42, ul. Pasteura 5 o godzinie 11:00

Carlos Perez-Sanchez (IFT UW)

Random surfaces V: Counting large maps

In string theory, quantum gravity, but also in pure mathematics, counting Riemann surfaces is crucial. Physicists tackled this problem using approximations of Riemann surfaces by "Large Maps", i.e. gluings of a large number of suitably small polygons. In this talk (based on chapter 5 of Eynard's book Counting Surfaces) we find their generating functions. The relation to Minimal Models and to Liouville gravity is exhibited (although the latter in less detail).

Zapraszamy do sali 5.42, ul. Pasteura 5 o godzinie 11:00

Helder Larraguivel (IFT UW)

Random Surfaces IV: Solving Tuttes-loop equations for matrix models

In our last episode we saw how to derive the loop equations for formal matrix integrals. Now following sections 3.1, 3.2 and 3.3 of B. Eynard's book (Counting Surfaces) we will learn how to solve the loop equations in two main steps. First, we solve for the two leading contributions, the disk and cylinder amplitudes. They are often referred to as unstable geometries because of their Euler characteristic being negative \xi < 0. Here we will introduce the notion of a spectral curve and its fundamental differential of the second kind. We will derive the spectral curves for the Gaussian, cubic and quartic matrix integrals. Second, we compute the remaining contributions. These are often called stable geometries because they are Rieman surfaces of genus g and n marked points with Euler characteristic \xi >=0. This is where the topological recursion appears, as recursion relations depend only on the topology of Riemann surfaces. We will finish with a couple of examples, the Gaussian and Airy matrix integrals. There we will notice that for two very different matrix integrals, they satisfy the same (topological) recursion relations but for different spectral curves. This is what is known as universality of topological recursion. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Aditya Bawane (IFT UW)

Random Surfaces III: Formal matrix integrals

We review formal matrix integrals and the combinatorics of expectation values. Following this we describe loop equations for formal matrix integrals and explain how they are related to map counting. We follow the second chapter of Eynard's "Counting Surfaces". Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Paweł Caputa (IFT UW)

Holographic Path Integral Optimization

I will talk about recent work arXiv:2104.00010 [hep-th] aimed at understanding path integral optimization holographically. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Aditya Bawane (IFT UW)

Random Surfaces II: Formal matrix integrals

Zapraszamy na spotkanie o godzinie 11:00

Miłosz Panfil (IFT UW)

O(n) models and category theory

We can view O(n) models, with n real, as an analytic continuation of O(N) models to non-integer values of N. This approach yields correct predictions, however it does not answer what O(n) symmetry actually is. I will discuss how the authors of [1] use category theory to answer this question. [1] D. J. Binder and S. Rychkov, "Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of O(N) Symmetry with Non-integer N", https://arxiv.org/abs/1911.07895. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Carlos Perez-Sanchez (IFT UW)

Random Surfaces I: On Combinatorial Maps and Tutte's equations

This is the first talk of the "Random Surfaces" series that will we talkplace fortnightly in the frame of the String Theory Journal Club. In this introductory talk we deal with combinatorial maps and prove Tutte's equations, which relate different generating series of maps recursively. We will mainly follow Eynard's 2016 book "Counting Surfaces", in this talk the first chapter. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Shi Cheng (IFT UW)

Mixed Chern-Simons levels and strip geometry for abelian 3d N=2

Following the logic of knot-quiver correspondence, it can be conjectured that unknot on strip geometry (strip Calabi-Yau manifold) corresponds to a 3d N=2 theory with gauge group U(1) * U(1) * ···* U(1) and mixed CS levels. However, it is well known in literature that strip geometry engineers a 3d N=2 theory with gauge group U (1) and some flavors. How could it be possible that the same geometry gives rise to two seemly different theories? We will show that these two different theories are actually dual to each other by mirror symmetry. We derive this result by using sphere partition functions and vortex partition functions. If time permits, we will discuss the correspondence between mixed CS levels and strip geometry. This presentation is based on https://arxiv.org/abs/2104.00713 and work in progress. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 17:30

Jorrit Kruthoff (Stanford University)

Classifying boundary conditions in JT gravity: from energy-branes to \alpha-branes

In this talk I will discuss various choices of boundary conditions in JT gravity. We will discuss the implications in the classical theory, the quantum mechanical path integral and comment on the interpretation in the matrix model definition of JT gravity.

Zapraszamy do sali 5.42, ul. Pasteura 5 o godzinie 11:00

Carlos Perez-Sanchez (IFT UW)

On random noncommutative geometry, multi-matrix models and free algebra

Random noncommutative geometry started in [Barrett-Glaser J. Phys. A 49(2016) 24] and can be seen as an approach to the quantisation of noncommutative geometry. Fuzzy geometries form a class of finite dimensional spectral triples whose spectral action can be computed in terms of noncommutative polynomials. After briefly explaining how, we focus on the algebraic structure of the Functional Renormalisation Group (RG) for multi-matrix models motivated by random noncommutative geometry, which turns out to be described by (a relative of) the free algebra. The motivation is to use this as a tool to find fixed points of the RG-flow, which are candidates for phase-transition. We finish with some progress on how to add matter fields. Based on arXiv:2007.10914. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Hesam Soltanpanahi (Jagiellonian University)

Exploring phase structure from the ground state QNEC

I use the quantum null energy condition in strongly coupled two dimensional field theories (QNEC2) as diagnostic tool to study a variety of phase structures, including crossover, second and first order phase transitions. A universal QNEC2 constraint for first order phase transitions with kinked entanglement entropy will be presented and I will discuss in general the relation between the QNEC2-inequality and monotonicity of the Casini–Huerta c-function. Then in a specific holographic example, I will show that evaluating QNEC2 for ground state solutions allows to predict the existence of phase transitions at finite temperature. Along the way I will discuss some universal behaviour which we found unexpectedly. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Syo Kamata (NCBJ)

On exact-WKB analysis, resurgent structure, and quantization conditions

There are two well-known approaches to studying nonperturbative aspects of quantum mechanical systems: saddle point analysis of the partition functions in Euclidean path integral formulation and the exact-WKB analysis based on the wave functions in the Schrödinger equation. In this work, based on the quantization conditions obtained from the exact-WKB method, we determine the relations between the two formalism and in particular show how the two Stokes phenomena are connected to each other: the Stokes phenomenon leading to the ambiguous contribution of different sectors of the path integral formulation corresponds to the change of the "topology" of the Stoke curves in the exact-WKB analysis. We also clarify the equivalence of different quantization conditions including Bohr-Sommerfeld, path integral and Gutzwiller’s ones. In particular, by reorganizing the exact quantization condition, we improve Gutzwiller’s analysis in a crucial way by bion contributions (incorporating complex periodic paths) and turn it into an exact result. Furthermore, we argue the novel meaning of quasi-moduli integral and provide a relation between the Maslov index and the intersection number of Lefschetz thimbles. This talk is based on: N.Sueishi, S.Kamata, T.Misumi and M.Unsal, "On exact-WKB analysis, resurgent structure, and quantization conditions," JHEP 12(2020)114, [arXiv:2008.00379 [hep-th]]. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Artur Strąg (IFT UW)

Deformations in two dimensional quantum field theory

A large class of two-dimensional quantum fields theories contain an interesting operator built from the stress tensor, called "TT-bar". Due to "TT-bar" many physically interesting quantities can be computed exactly and explicitly in terms of the data from the undeformed theory, such as the S-matrix and the finite-volume spectrum. In my talk I will give a short introduction to the "TT-bar" deformations. I discuss some examples of applications of "TT-bar".

Zapraszamy na spotkanie o godzinie 11:00

Helder Larraguivel (IFT UW)

From dualities between 3d N=2 theories to new colorful knot symmetries

The goal of this talk is to present a new set of symmetries for colored HOMFLY-PT knot invariants and their implications as dualities in the 3d - 3d correspondence. These are the results of joint work with Piotr Sułkowski, Jakub Jankowski, Piotr Kucharski and Dmitry Noshchenko. For the overture, we will review how the set of 3d N = 2 gauge theories arising from string compactification can be described in terms of a quiver diagram (directed graph). We will use scalar QED as the simplest example. Then, in the intermezzo, we will see how dualities between 3d theories naturally arise from operations on the quiver diagram. These operations are manifestations of the pentagon identity for the quantum dilogarithm. For our gran finalle, we will find that these dualities for certain quivers lead to new symmetries for knot invariants. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Jan Dereziński (KMMF)

Homogeneous Schroedinger operators and the Lie algebra sl(2,R)

Homogeneous Schroedinger operators, called also Bessel operators are given by $H_m=-\partial_x^2+(-\frac14+m^2\frac{1}{x^{2}},$with the boundary condition $\sim x^{m+\frac12}$ near $0$. I will discuss their role in representations of the smallest semi-simple non-compact Lie group $SL(2,R)$. The (time-dependent) file with my presentation can be found at https://www.fuw.edu.pl/~derezins/sl2r-slides.pdf. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Adam Bzowski (University of Crete)

Consistency of supersymmetric 't Hooft anomalies

We consider recent claims that supersymmetry is anomalous in the presence of a R-symmetry anomaly. We revisit arguments that such an anomaly in supersymmetry can be removed and write down an explicit counterterm that accomplishes it. Removal of the supersymmetry anomaly requires enlarging the corresponding current multiplet. As a consequence the Ward identities for other symmetries that are already anomalous acquire extra terms. This procedure can only be impeded when the choice of current multiplet is forced. We show how Wess-Zumino consistency conditions are modified when the anomaly is removed. Finally we check that the modified Wess-Zumino consistency conditions are satisfied, and supersymmetry unbroken, in an explicit one loop computation using Pauli-Villars regulators. To this end we comment on how to use Pauli-Villars to regulate correlators of components of (super)current multiplets in a manifestly supersymmetric way. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Dimitrios Patramanis (IFT UW)

Berry picking in the holographic forest

After briefly reviewing the notions of Berry’s phase and coadjoint orbits I will be explaining how these arise in a holographic setup. Namely, I will be talking about the modular Berry phase arising in AdS3/CFT2 and the prospects of its generalization in the broader context of the Banados geometries. To this end I will be discussing the different tools and methods required to do so and attempt to highlight their utility in addressing problems in general. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Dmitry Noshchenko (IFT UW)

The "Geometric" recursion

We review the famous paper by Maryam Mirzakhani: "Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces", Invent. Math., 167(1):179– 222, 2007. In the first part, we introduce all necessary ingredients: moduli space of Riemann surfaces, Teichmuller space, mapping class group, pairs of pants and then move to McShane identity for length of simple closed geodesics. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Aditya Bawane (IFT UW)

Topological recursion: A brief excursion, part II

We introduce topological recursion, and illustrate it's machinery with the example of the Airy curve. We discuss its general properties, followed by its graphical representations, further generalizations, and if time permits, quantum Airy structures. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Aditya Bawane (IFT UW)

Topological recursion: A brief excursion

Zapraszamy na spotkanie o godzinie 11:00

Jan Boruch (IFT UW)

Basics of JT gravity

I will review some basic aspects of JT gravity relevant for "JT gravity as a matrix integral" paper. We will also go through the computations of the JT path integral for the disk and the trumpet geometries. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Paweł Caputa (IFT UW)

2d gravity, Liouville theory and matrix models - Old Story, part II

I will review some relevant aspects of 2d gravity, Liouville theory and matrix models that may serve as a relevant background for our "JT gravity as matrix integral" story. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Paweł Caputa (IFT UW)

2d gravity, Liouville theory and matrix models - Old Story

Zapraszamy na spotkanie o godzinie 11:00

Carlos Perez-Sanchez (IFT UW)

Random matrices techniques in JT-gravity

In this first talk of the JT-gravity seminar series, I will elaborate on the matrix models tools used in JT gravity by Saad-Shenker-Stanford in arXiv:1903.11115. If time allows, some aspects of the (closely related) SYK-model will be addressed too. Link: meet.google.com/gbj-tmns-err

Zapraszamy na spotkanie o godzinie 11:00

Aditya Bawane (IFT UW)

A survey of AGT correspondence

The AGT correspondence relates N = 2 supersymmetric gauge theories on 4-dimensional manifolds to Liouville field theory, a 2-dimensional conformal field theory. In this talk, I will survey some of the necessary ingredients like rigid N=2 supersymmetry on curved manifolds, supersymmetric localization, and amplitudes in Liouville theory, following which I will summarize some key results in AGT correspondence, including some relatively recent works establishing the correspondence for boundary states and loop operators in gauge theory. Link: meet.google.com/gbj-tmns-err

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 11:00

Dongsheng Ge (IFT UW)

Holographic defect model and quantum complexity

In this talk, I will start with an introduction of the holographic defect model, which is a domain wall geometry with a one-dimensional lower tensile AdS brane. By considering the boundary graviton scattering process in AdS_3, you will see that the brane tension is dual to the energy transport coefficients on the CFT side, instead of the boundary entropy which has been commonly believed. In the second part, I will move to the holographic consideration of a quantity from quantum information theory which is called quantum complexity. The same holographic defect model will be used to quest for the universality of the two holographic conjectures “Complexity = Volume” and “Complexity = Action”. Though a definite answer can not be reached in the current scope, I will make some comments based on our preliminary field theory complexity considerations.

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 11:00

(IFT UW)

Matrix models, JT gravity, and beyond

Matrix models, JT gravity, and beyond...

Zapraszamy do sali 5.42, ul. Pasteura 5 o godzinie 14:00

Edward Witten – video (IAS)

Volumes and Random Matrices

I will describe recent results relating two-dimensional gravity and supergravity; volumes of moduli spaces of Riemann surfaces and super Riemann surfaces; and random matrix ensembles. See https://arxiv.org/abs/1903.11115 by Saad, Shenker, and Stanford; https://arxiv.org/abs/1907.03363 by Stanford and me.