Gauged Linear Sigma Models

29 Jun 2026, 09:30 → 3 Jul 2026, 17:00 Europe/Berlin

02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

Registration closed on 02 March 2026.

 

One of the most important tools to quantitatively describe families of two-dimensional conformal field theories are gauged linear sigma models (GLSMs). As such they offer a powerful and indispensable method to study string compactifications and their phase structures from a worldsheet perspective. Over the years, the scope of GLSMs has developed much further, namely not only as a methodology to study string theories, but also to address fundamental questions of (supersymmetric) quantum field theories, in particular in two, three and four dimensions. That is to say, GLSMs have provided key insights into numerous aspects of mathematical physics, offering a bridge to various fields in mathematics such as enumerative and algebraic geometry and category theory. The aim of this workshop is to bring together experts from physics and mathematics in order to address topical research questions and to identify new applications for GLSMs. 

Monday 29 June

09:30 Check-in

1 Cyril Closset, TBA

Speaker: Cyril Closset

11:00 Break

2 Ilka Brunner, TBA

Speaker: Ilka Brunner

14:30 Break

3 Thorsten Schimmanek

Speaker: Thorsten Schimmanek

Tuesday 30 June

4 Albrecht Klemm, Fibering out Calabi-Yau motives

Speaker: Albrecht Klemm

10:30 Break

5 Ed Segal, TBA

Speaker: Ed Segal

6 Pyry Kuusela, Physics Applications of Hodge Theory and Arithmetic Geometry

This talk is an overview of recent progress in applying techniques from arithmetic geometry to physics. Many interesting physics constructions in various theories, such as CFTs and SUGRAs, can be related to non-trivial Hodge theoretic problems. Some number theoretic results and conjectures, generalising the celebrated modularity theorem in various directions, imply that these problems can be solved by using arithmetic geometry. After reviewing these connections, I give a quick overview of techniques I have developed together with collaborators to efficiently compute arithmetic geometry data, and give various examples of applications to physics.

Time permitting, I will give some comments on recent work, questions, and speculation on how the correspondence between arithmetic geometry and physics can be taken beyond the context of Hodge theory.

Speaker: Pyry Kuusela

14:30 Break

7 Yann Proto, Phases of linear sigma models with torsion

I will describe joint work with D. Israël and I. Melnikov on (0,2) gauged linear sigma models relevant for heterotic flux compactifications. An important class of flux backgrounds is realized as a torus fibration over K3 with a stable holomorphic vector bundle. I will present torsional GLSMs whose large radius phase describes such a geometry with a trivial gauge bundle, and which admit a Landau–Ginzburg orbifold phase. I will also discuss related (0,2) constructions for Calabi–Yau compactifications with line bundles.

Speaker: Yann Proto

Wednesday 1 July

8 Xiaohan Yan, Quantum K-theory of GIT quotients

The K-theoretic Gromov-Witten (KGW) invariants are deformation invariants of a complex variety defined by counting curves, generalizing the more familiar Gromov-Witten invariants. In this talk, I discuss my work on the generating function of the genus-zero KGW invariants of type-A flag varieties, a computation motivated by the 3D mirror symmetry. The method is based on the idea of abelian/non-abelian correspondence. I also discuss further applications of this method in studying the KGW invariants of GIT quotients and their associated q-difference equations.

Speaker: Xiaohan Yan

10:30 Break

9 YP Lee, Quantum elliptic cohomology: a progress report

Among the generalized cohomology theories associated with 1-dimensional groups are ordinary cohomology (additive group), complex K-theory (multiplicative group), and elliptic cohomology (elliptic curve). In the late 1980s and early 1990s, physicists initiated quantum cohomology (Gromov-Witten theory) as the enumerative geometry associated with ordinary cohomology. A decade later, A. Givental and I introduced quantum K-theory. In this joint work with E. Bouaziz and I. Huq-Kuruvilla, I will report on recent progress toward establishing a mathematical framework for quantum elliptic cohomology.

Speaker: YP Lee

10 Kentaro Hori, TBA

Speaker: Kentaro Hori

14:30 Break

11 Jirui Guo, Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double β-Grothendieck polynomials

The GL(N) asymmetric five vertex model is an integrable system that generalizes the spin-1/2 five vertex model. In this talk, I will explain why the Bethe ansatz equations of this model encode the ring relations of the equivariant quantum cohomology and K-theory ring of partial flag varieties, which are the OPE rings of the 2D and 3D quiver GLSMs. I will also show how the Bethe ansatz states of the integrable model generate the double β-Grothendieck polynomials interpolating the double Schubert polynomials and the double Grothendieck polynomials, which are representatives of the Schubert classes.

Speaker: Jirui Guo

Thursday 2 July

12 Tyler Kelly, TBA

Speaker: Tyler Kelly

10:30 Break

13 Chiu-Chu Melissa Liu, Extended Landau-Ginzburg/Calabi-Yau correspondence and open/closed correspondence for the quintic threefold

Chiodo-Ruan proved genus-zero Landau-Ginzburg/Calabi-Yau (LG/CY) correspondence for the quintic Calabi-Yau threefold, which relates genus-zero Fan-Jarvis-Ruan-Witten (FJRW) invariants of the Fermat quintic polynomial in five variables and genus-zero Gromov-Witten (GW) invariants of the quintic Calabi-Yau threefold. This correspondence can be viewed as an example of GIT wall-crossing in a gauged linear sigma model (GLSM). I will explain results and conjectures on (1) extending this correspondence to genus-zero open FJRW invariants and genus-zero open GW invariants of the quintic Calabi-Yau threefold, and (2) open/closed correspondence relating the above genus-zero open GW (resp. FJRW) invariants and closed GLSM invariants of a specific GLSM, the extended quintic GLSM, in the positive (resp. negative) phase. This is based on joint work with Konstantin Aleshkin.

Speaker: Melissa Liu

14:30 Break

Friday 3 July

14 Emanuel Scheidegger, TBA

Speaker: Emanuel Scheidegger

10:30 Break

15 Ilarion Melnikov, The spectral flow operator in (2,2) Calabi-Yau GLSMs

The (2,2) GLSM Lagrangian allows for a simple presentation of a number of deformations of the IR SCFT obtained as the endpoint of the RG flow defined by the gauge theory path integral.
Typically, this only covers a subset of the deformations. In this talk I will review some work on describing the missing, so-called “non-toric” and “non-polynomial”, deformations as operators in the chiral algebra of the Lagrangian theory, and I will explain the key challenge through a construction, found together with Ronen Plesser, of a special holomorphic operator—the chiral spectral flow operator—in terms of the GLSM fields.

Speaker: Ilarion Melnikov

14:00 Break; in-person checkout by 14:30.