Decomposition 2021

May 22, 2021, 8:00 AM → May 23, 2021, 10:50 PM US/Eastern

This is an online (zoom) workshop on "decomposition," which states that two-dimensional QFTs with finite global 1-form symmetries are equivalent to disjoint unions of QFTs without 1-form symmetries.  Decomposition was first described in hep-th/0606034, to understand properties of 2d continuum theories with finite 1-form symmetries such as the CP^n model with nonminimal charges, as originally described in hep-th/0502027, 0502044, 0502053.

Speakers will include

• H-H Tseng (Ohio State University), on his and his collaborators' work from 2008 onwards on applications to Gromov-Witten invariants of gerbes, see for example arXiv:0812.4477, 0907.2087,
• Mauricio Romo (Tsinghua) on applications to gauged linear sigma models (GLSMs).  One of the original applications of decomposition was to understand phases of certain GLSMs, where locally there is a finite 1-form symmetry which leads to a (nonperturbative) description as a branched cover (arXiv:0709.3855). Mauricio will discuss current developments, as in his paper arXiv:2012.14109.
• Richard Eager (KIAS), on his recent work (arXiv:2009.03907) on elliptic genus computations in supersymmetric two-dimensional gauge theories and the role of decomposition,
• Daniel Robbins (SUNY Albany), on his recent work (arXiv:2101.11619) on generalizations of decomposition in orbifolds,
• Yuya Tanizaki (Yukawa Inst. Kyoto), on analogues of decomposition in four-dimensional gauge theories with three-form symmetries (arXiv:1912.01033),
• Theodore Jacobson (Univ. Minnesota) on his recent work on vacua in universes (arXiv:2012.10555),
• Zohar Komargodski (SUNY Stony Brook), on his recent work (arXiv:2008.07567) and its role in decomposition.

The schedule has been posted; all times are US eastern time.  We intend to record video, so that participants can watch asynchronously.

Registration is now open.  We ask that anyone who wishes to participate register in advance (use the registration link on this website).  We will send out zoom links a few days before the workshop beings to all registered participants. 

 

Code of conduct:  This event is committed to providing a harassment-free conference experience for everyone, regardless of race, ethnicity, gender, gender identity and expression, age, sexual orientation, disability, physical appearance, body size, religion or lack thereof. We do not tolerate harassment of event participants in any form in any event venue, including any online media.  Participants violating these rules may be sanctioned or expelled from the event.

 

Saturday, May 22

1 Welcome / orientation

2 Yuya Tanizaki: Modified instanton sum in 4d gauge theories

Abstract: In the path integral formulation of quantum field theories (QFTs), we are supposed to sum up all possible field configurations to ensure the locality in the usual lore. In the case of 4d gauge theories, this would require us to sum up all the instanton sectors, which topologically classify the gauge-field configurations in the closed spacetime. However, it turns out that this is not mandatory, and there are other consistent choices to define QFTs. We show that restricting the instanton sectors can be consistent with locality as a consequence of "Decomposition". Starting from a brief review of the decomposition in 2d QFTs, we will tell how this interesting property can be generalized to higher-dimensional QFTs, and also explain the concrete example using 4d Yang-Mills theory.

Decomposition2021_Tanizaki.pdf

video

3 Mauricio Romo: A GLSM view on Homological Projective Duality

Abstract: I will present a rather general construction of homological projective dual (HPD) pairs using gauged linear sigma models. In mathematical terms, HPD can be viewed as a tool to generate semiorthogonal decompositions. In physical terms, HPD pairs are phases of GLSMs whose categories of B-branes are related in a very precise way (and if some conditions are met, equivalent). I will mostly focus on the abelian case and, if time permits, will present a few remarks for the nonabelian case. This is based on joint work with Z. Chen and J. Guo: 2012.14109.

Romo_talk_decomp.pdf

video

4 Theodore Jacobson: Lifetimes of near-eternal false vacua

Abstract: We consider examples of extremely long lived false vacua which arise in theories with approximate or emergent (d-1)-form symmetries. In the limit that these symmetries are exact, decomposition of the theory into 'universes' implies that certain false vacua are exactly stable. We look at cases where the false vacua in question arise near symmetric points in parameter space where the (d-1)-form symmetry participates in a 't Hooft anomaly with an ordinary global symmetry. The effects of explicit symmetry-breaking deformations, which obstruct exact decomposition, are considered in a simple quantum mechanical model and in the Schwinger model.

decomposition_slides_jacobson.pdf

video

5 Daniel Robbins: Decomposition in orbifolds with discrete torsion

Abstract: In the context of 2D CFT, decomposition occurs when we construct an orbifold of a theory by a group G that has a trivially-acting subgroup K. The resulting theory is a disjoint union of orbifolds by subgroups of the effective G/K symmetry. We'll describe how turning on discrete torsion in G affects the story, including opening the possibility that the disjoint union contains only a single term. We will also discuss some work in progress relating these ideas to quantum symmetries and anomalies.

Decomposition_Robbins.pdf

video

Sunday, May 23

6 Richard Eager: Elliptic genera of pure gauge theories in two dimensions

Abstract: I will explain how to compute the elliptic genera of (2,2) supersymmetric gauge theories in two dimensions with gauge group G/Gamma (for G semisimple and simply-connected, Gamma a subgroup of the center of G) with various discrete theta angles. The two new ingredients are a systematic study of the moduli space of flat G/Gamma connections on the torus and an efficient organization of the supersymmetric localization computation using the classification of nilpotent orbits. The elliptic genera are consistent with expectations from decomposition of two-dimensional theories with finite global one-form symmetries and with computations of supersymmetry breaking for some discrete theta angles in pure gauge theories.

Decomposition-Eager.pdf

video

7 Hsian-Hua Tseng: On the Gromov-Witten theory of etale gerbes

Abstract: We aim to give a review of results on how Gromov-Witten invariants of etale gerbes respect the decomposition conjecture, from the speaker's own perspective.

GWgerbeTalk-Tseng.pdf

video

8 Zohar Komargodski

video