Topological String Theory and Related Topics

Europe/Zurich
4/3-006 - TH Conference Room (CERN)

4/3-006 - TH Conference Room

CERN

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Description

Short description

The first week of the Institute will primarily focus on non-perturbative topological string theory, refinement, exact quantisation and matrix models, while the second week will deal with B-type topological string theory, open-closed mirror symmetry and categories of matrix factorisations. One of the goals of the second week is to bring together researchers in both Mathematics and Physics.

This informal workshop will have just 2-3 talks per day to allow for extensive discussions and collaboration. It is supported jointly by CERN and by the Korean government under the CERN-Korea Collaboration agreement. It is also supported by the IBS Center for Geometry and Physics, Korea.

Organisers: Ahmad Zein Assi, Alba Grassi, Cheol-Hyun Cho, Calin Lazaroiu,  Sangmin Lee, Wolfgang Lerche, Marcos Marino, Nikita Nekrasov, Yong-Geun Oh and Johannes Walcher.

Key speakers

1st week: A. Klemm, K. S. Narain, R. Schiappa

2nd week: C.-H. Cho, J.-S. Park and J. Solomon

Practical information: There is no registration fee, and participation is open except for limited desk space.  A limited number of rooms have already been pre-booked at CERN hotels, please contact THworkshops.secretariat@cern.ch (after registration) if you want to stay there during the meeting.

Registration:  Closed 

Extended description

Topological string theory has played an important role in the past decades in inducing a deeper understanding of string theory, but has also led to a plethora of new results and applications both in mathematics and physics.

From the mathematical point of view, this theory is deeply related to matrix models, arithmetic and integrability, spectral theory, supersymmetric gauge theories, Painlevé equations, knot theory and homological mirror symmetry. These relations have been exploited in recent years leading to important developments in these fields. For instance it has been possible to compute exactly and explicitly the spectrum of a new class of operators and integrable systems or to analyse in detail certain non-perturbative effects in supersymmetric gauge and string theories, and matrix models. Important progress has also been made in understanding topological open string invariants via mirror symmetry.

On the other hand, from the physical point of view, topological string theory has had a direct impact on the understanding of the physical string theory from which it can be constructed. Indeed, it can be viewed as a toy model for string theory probing its BPS sector only. For example, it has been shown that the partition function of topological string theory computes a class of higher derivative gravitational couplings in the string effective action. At low energies, this connection has led to new insights into Seiberg-Witten theory and its deformations. In a similar vein, there is still a number of interesting problems and challenges, one of which is to provide a clear worldsheet definition of the refined topological string and its applications to the physics of black holes.

The goal of the institute is to bring together mathematicians and physicists working on topics related to topological string theory and to give an overview of the recent developments over the last years. This will help in fostering new collaborations by providing a stimulating environment to make further advancements in the field.

Participants
  • Aditya Bawane
  • Ahmad Zein Assi
  • Alba Grassi
  • Albrecht Klemm
  • Alessandro Tanzini
  • Alexander Aleksandrov
  • Amer Iqbal
  • Amir-Kian Kashani-Poor
  • Andrei Marshakov
  • Calin Lazaroiu
  • Camillo Imbimbo
  • Carlo Angelantonj
  • Elena Mirela Babalic
  • Emanuel Scheidegger
  • Fabrizio Del Monte
  • Giulio Bonelli
  • Guglielmo Lockhart
  • Ingmar Saberi
  • Ioannis Florakis
  • Jae-Suk Park
  • Jake Solomon
  • Jie Gu
  • Johanna Knapp
  • Johannes Walcher
  • Jörg Teschner
  • Kaiwen Sun
  • Kumar Shiv Narain
  • Madhav Sapkota
  • Marcos Marino Beiras
  • Murad Alim
  • Piotr Sulkowski
  • Ricardo Schiappa
  • Seungjoon Hyun
  • Simeon Hellerman
  • Stefan Hohenegger
  • Thorsten Schimannek
  • VIVEK SINGH
  • Wolfgang Lerche
  • XIN WANG
  • Yasuyuki Hatsuda
  • Yong-Geun Oh
    • 9:00 AM 9:30 AM
      Registration 30m 4-2-004 (TH Secretariat)

      4-2-004

      TH Secretariat

    • 9:30 AM 10:30 AM
      A review on non-perturbative topological string theory and its applications 1h 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      In this talk I will review a non-perturbative definition of topological string theory and discuss some of its applications.
      I will explain how this construction is related to blowup equations (see talk by Gu), the Hofstadter butterfly problem (see talk by Hatsuda) and the theory of Painlevé equations (see talks by Marshakov, Teschner and Del Monte

      Speaker: Alba Grassi (U)
    • 10:30 AM 11:00 AM
      Coffee Break 30m 4/2-011 - TH common room

      4/2-011 - TH common room

      CERN

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    • 11:00 AM 11:30 AM
      Electrons on the honeycomb lattice and topological strings 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      I would like to briefly review our recent works on an application of topological string theory to 2d electron system. I will explain how to generalize this idea to the case of honeycomb lattice.

      Speaker: Yasuyuki Hatsuda (Department of Physics, Rikkyo University)
    • 11:30 AM 12:00 PM
      Solving refined BPS invariants with blowup equations 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      Speaker: Jie Gu (University of Geneva)
    • 6:00 PM 7:00 PM
      Cocktail 1h Glassbox

      Glassbox

    • 9:00 AM 10:00 AM
      Topological String and String effective couplings 1h 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      We will review the relation between Topological String Theory and the physical string couplings in the context of Type II string theories. Mapping the problem to physical string couplings allows one to study their dual heterotic theories that give rise to Schwinger like formulae for the singularity structures due to the appearance of massless BPS states. In this context we also discuss the refined topological string and present some new perspectives and open questions.

      Speaker: Kumar Narain (ICTP)
    • 10:00 AM 10:30 AM
      Coffee Break 30m 4/2-011 - TH common room

      4/2-011 - TH common room

      CERN

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    • 10:30 AM 11:00 AM
      The Geometry Behind Topological Amplitudes 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      Speaker: Carlo Angelantonj
    • 9:00 AM 10:00 AM
      Topological strings, knots and quivers 1h 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      I will review a recently discovered correspondence between
      topological strings (and knots and their invariants in particular) and quiver representation theory.

      Speaker: Piotr Sulkowski
    • 10:00 AM 10:30 AM
      Coffee Break 30m 4/2-011 - TH common room

      4/2-011 - TH common room

      CERN

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    • 10:30 AM 11:00 AM
      Identifying matter in F-theory via the topological string 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      Speaker: Amir-Kian Kashani-Poor
    • 2:00 PM 3:15 PM
      Resurgence, Matrices, and Strings (TH Colloquium) 1h 15m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      Perturbation theory is generically divergent, leading to series with zero radius of convergence. When such asymptotic perturbative-series are resurgent, this problem can be tackled by extending the perturbative series into a non-perturbative trans-series, in a specified fashion. Resurgent trans-series may then be used to go beyond perturbation theory in generic problems across theoretical physics, and address diverse non-perturbative phenomena. This colloquium will cover a brief introduction to resurgence and trans-series, with some illustrative applications within (zero-dimensional) gauge theories (i.e., matrix models) and (topological) string-theoretic settings

      Speaker: Ricardo Pina Schiappa De Carvalho (Universidade de Lisboa (PT))
    • 9:00 AM 10:00 AM
      Topological String on Elliptic Calabi-Yau 3-folds and 6d SCFT 1h 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      We describe four methods to solve the topological string on elliptic Calabi-Yau manifolds and its relation to 6d SCFT.

      Speaker: Albrecht Klemm (Institut fuer Theoretische Physik)
    • 10:00 AM 10:30 AM
      Coffee Break 30m 4/2-011 - TH common room

      4/2-011 - TH common room

      CERN

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    • 10:30 AM 11:00 AM
      BPS variation of Hodge structure 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      The existence, decay and formation of BPS bound-states in N=2 theories are controlled by the central charge function through the notion of Pi-stability. In this talk I will describe the variation of the central charge over the moduli space of a given theory introducing a notion of BPS variation of Hodge structure. This description leads to exact results, giving exact descriptions of the walls of marginal stability and sheds new light on the attractor flow as a tool to solve the BPS problem. This is based on joint work with Florian Beck, Anna Biggs and Daniel Bryan.

      Speaker: Murad Alim (University of Hamburg)
    • 9:00 AM 9:45 AM
      Triality in Little String Theories 45m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      I discuss a class of little string theories (LSTs) with eight supercharges on the world-volume of N M5-branes probing a transverse Z_M orbifold. These M-brane configurations compactified on a circle are dual to M D5-branes intersecting N NS5-branes on T^2 x R^{7,1} as well as to F-theory compactified on a toric Calabi-Yau threefold X_{N,M}. I argue that the Kähler cone of X_{N,M} admits three regions associated with weakly coupled quiver gauge theories of gauge groups [U(N)]^M, [U(M)]^N and [U(NM/k)]^k where k=gcd(N,M). These provide low-energy descriptions of different LSTs. The duality between the first two gauge theories is well known and is a consequence of the S-duality between D5- and NS5-branes or the T-duality of the LSTs. The triality involving the third gauge theory is new and I demonstrate it using several examples. Finally, I argue that triality implies a dihedral symmetry for the theories with M=1, which acts intrinsically non-perturbative from a gauge theory perspective.

      Speaker: Stefan Hohenegger (Centre National de la Recherche Scientifique (FR))
    • 9:45 AM 10:30 AM
      Coffee Break 45m 4/2-011 - TH common room

      4/2-011 - TH common room

      CERN

      9
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    • 10:30 AM 11:15 AM
      Chiral algebras, instanton strings, and hidden symmetries 45m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      I will discuss a class of 2d NLSMs which describe D3 branes wrapped on a two-sphere and probing an F-theory singularity. The chiral algebras of the NLSMs turn out to be a very useful tool. For one choice of twisting, the resulting NLSMs describe 6d instanton strings, and the chiral algebras encode BPS invariants of elliptic threefolds. A different choice of twist leads to NSLMs on minuscule varieties; in one notable example, the chiral algebra of the NLSM describes the ghost sector of the pure spinor superstring, and our construction reveals the existence of a hidden E6 symmetry.

      Speaker: Guglielmo Lockhart
    • 9:00 AM 10:00 AM
      Cluster integrable systems, supersymmetric gauge theories and topological strings 1h 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      Speaker: Andrei Marshakov (Center for Advanced Studies, Skoltech)
    • 10:00 AM 10:30 AM
      Coffee Break 30m 4/2-011 - TH common room

      4/2-011 - TH common room

      CERN

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    • 10:30 AM 11:00 AM
      Painlevé/Gauge theory correspondence on the torus 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      In the last few years there have been many new results connecting (linear quiver) N=2 class S theories, and the topological strings that engineeer them, to the theory of isomonodromic deformations on the sphere and their q-deformations.
      The aim of this talk is to show how this connection can be extended beyond the case of genus zero, which corresponds to circular quiver gauge theories, including adjoint hypermultiplets in the description. We will see how the genus one case displays new qualitative features that are absent on the sphere, due to the possibility of various inequivalent vector bundles, and how this actually provides new interesting relations satisfied by the 4d all genus Topological String partition function.

      Speaker: Fabrizio Del Monte (SISSA, Trieste)
    • 11:00 AM 11:30 AM
      Partition functions from quantum curves 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      In joint work with I. Coman and E. Pomoni we had recently proposed a definition of the topological string
      partition functions for the local Calabi-Yau manifolds used in
      the geometric engineering of N=2, d=4 class S field theories.
      The main goal of my talk will be to review this proposal, and
      to explain how the exact WKB method provides a crucial
      ingredient. We thereby arrive at a fully non-perturbative
      construction of the partition functions from the classical
      curves describing the relevant B-model backgrounds.

      Speaker: Joerg Teschner (DESY)
    • 9:00 AM 10:00 AM
      Gromov-Witten-Floer theory and mirror symmetry 1h 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      In this talk I will first review the Lagrangian Floer theory in the general context of open-closed TFT in two dimensions and then explain its application to the mirror symmetry of compact toric manifolds. In particular, I will explain construction of a natural isomorphism between the Frobenius manifold structures of the (big) quantum cohomology of a toric manifold and of Saito's theory of singularities of the potential function constructed via the bulk-deformed Floer cohomology. Our proof of the isomorphism involves the open-closed Gromov-Witten theory of one-loop. This talk is based on a series of joint works with Fukaya, Ohta and Ono.

      Speaker: Yong-Geun Oh (Postec)
    • 10:00 AM 10:30 AM
      Coffee Break 30m 4/2-011 - TH common room

      4/2-011 - TH common room

      CERN

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    • 10:30 AM 11:00 AM
      The general theory of B-type Landu-Ginburg models 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      I give a very brief review of the main points of my recent work on the constructive field theory of the most general class of B-type Landau-Ginzburg models, stressing the conceptually important parts while avoiding most of the mathematical details.

      Speaker: Calin Lazaroiu (Institute for Basic Science, Center for Geometry and Physics)
    • 11:00 AM 11:30 AM
      Open intersection numbers, matrix models and W-constraints 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      In their recent work R. Panharipande, J. Solomon and R.
      Tessler constructed intersection theory on the moduli spaces of
      Riemann surfaces with boundaries. The goal of my talk is to describe
      the generating function of this theory, which is a simplest example of
      the open topological string model, in terms of matrix models and
      integrable hierarchies. The geometrical description of the open theory
      is much more complicated then the closed one, however, on the level of
      matrix
      models and integrable systems the difference is not so dramatic and
      the open case can be described by a natural deformation of the
      Kontsevich-Witten model.

      Speaker: Alexander Alexandrov (CGP IBS)
    • 9:00 AM 10:00 AM
      Bounding Chains in Open Gromov-Witten Theory 1h 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      I will discuss an approach to establishing the foundations of open Gromov-Witten theory based on bounding chains and Fukaya A-infinity algebras.

      Speaker: Jake Solomon (Hebrew University)
    • 10:00 AM 10:30 AM
      Coffee Break 30m 4/2-011 - TH common room

      4/2-011 - TH common room

      CERN

      9
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    • 10:30 AM 11:00 AM
      Periods and quasiperiods of modular forms and the mirror quintic at the conifold 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      We exhibit a relation between the analytic continuation of the periods of the mirror quintic to the conifold and periods and quasiperiods of a certain weight 4 Hecke eigenform associated to the mirror quintic. To explain this, we review the theory of periods of modular forms and extend it to quasiperiods.

      Speaker: Emanuel Scheidegger (Universitaet Augsburg)
    • 6:00 PM 7:00 PM
      Cocktail 1h Glassbox

      Glassbox

    • 9:00 AM 10:00 AM
      BV quantization and special coordinates in quantum field theory 1h 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      We show that there is a universal algebraic structure, closely related with that of the WDVV equation, governing quantum correlation functions of every quantum field theory based on the BV quantization scheme.

      Speaker: Jae-Suk Park (Postec)
    • 10:00 AM 10:30 AM
      Coffee Break 30m 4/2-011 - TH common room

      4/2-011 - TH common room

      CERN

      9
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    • 10:30 AM 11:00 AM
      Sphere partition function and the refined swampland distance conjecture 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      The sphere partition function of the gauged linear sigma model computes the exact metric on the Kaehler moduli space of a Calabi-Yau. We use this to test the refined swampland distance conjecture for examples of one-parameter Calabi-Yau threefolds with exotic hybrid points. This is joint work with David Erkinger.

      Speaker: Johanna Knapp (TU Wien)
    • 11:00 AM 11:30 AM
      Modularity from Monodromy 30m 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      We discuss the relation between certain auto-equivalences of the category of B-branes on elliptic Calabi-Yau threefolds and modular properties of the corresponding topological string partition function.
      This suggests a geometric explanation and generalization of recent conjectures on the appearance of lattice Jacobi forms.
      In particular, we will shed light on the special case where the fibration does not have a section but only multi-sections.

      Speaker: Thorsten Schimannek (University of Vienna)
    • 9:00 AM 10:00 AM
      Matrix Factorizations and Homological Mirror Symmetry 1h 4/3-006 - TH Conference Room

      4/3-006 - TH Conference Room

      CERN

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      I will review how matrix factorizations can be used to do computations in homological mirror symmetry and show that a crucial ingredient is a generalization of Saito's residue pairings to boundaries.

      Speaker: Wolfgang Lerche (CERN)