A correction to this paper has been published: https://doi.org/10.1007/JHEP07(2023)120

United Kingdom

Alejandra Castro

Netherlands

Japan

Ioana Coman

Jackson Fliss

United States

Claire Zukowski

Erratum to: Keeping matter in the loop in dS3 quantum gravity

We propose a mechanism that couples matter fields to three-dimensional quantum gravity, which can be used for theories with a positive or negative cosmological constant. Our proposal is rooted in the Chern-Simons formulation of three-dimensional gravity and makes use of the Wilson spool, a collection of Wilson loops winding around closed paths of the background. We show that the Wilson spool correctly reproduces the one-loop determinant of a free massive scalar field on rotating black holes in <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> and Euclidean <math><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> as <math><msub><mi>G</mi><mi>N</mi></msub><mo>→</mo><mn>0</mn></math>. Moreover, we describe how to incorporate quantum metric fluctuations into this formalism.

Jackson R. Fliss

Coupling Fields to 3D Quantum Gravity via Chern-Simons Theory

We propose a mechanism that couples matter fields to three-dimensional de Sitter quantum gravity. Our construction is based on the Chern-Simons formulation of three-dimensional Euclidean gravity, and it centers on a collection of Wilson loops winding around Euclidean de Sitter space. We coin this object a Wilson spool. To construct the spool, we build novel representations of 𝔰𝔲(2). To evaluate the spool, we adapt and exploit several known exact results in Chern-Simons theory. Our proposal correctly reproduces the one-loop determinant of a free massive scalar field on S 3 as G  N  → 0. Moreover, allowing for quantum metric fluctuations, it can be systematically evaluated to any order in perturbation theory.

Keeping matter in the loop in dS3 quantum gravity

In this paper we investigate the relation between conformal blocks of Liouville CFT and the topological string partition functions of the rank one trinion theory T 2. The partition functions exhibit jumps when passing from one chamber in the parameter space to another. Such jumps can be attributed to a change of the integration contour in the free field representation of Liouville conformal blocks. We compare the partition functions of the T 2 theories representing trifundamental half hypermultiplets in N = 2, d = 4 field theories to the partition functions associated to bifundamental hypermultiplets. We find that both are related to the same Liouville conformal blocks up to inessential factors. In order to establish this picture we combine and compare results obtained using topological vertex techniques, matrix models and topological recursion. We furthermore check that the partition functions obtained by gluing two T 2 vertices can be represented in terms of a four point Liouville conformal block. Our results indicate that the T 2 vertex offers a useful starting point for developing an analog of the instanton calculus for SUSY gauge theories with trifundamental hypermultiplets.

Germany

Elli Pomoni

Joerg Teschner

Trinion conformal blocks from topological strings

We study the Coulomb branch of class S k $$ {\mathcal{S}}_k $$ N $$ \mathcal{N} $$ = 1 SCFTs by constructing and analyzing their spectral curves.

Romania

Greece

Masato Taki

South Korea

Futoshi Yagi

Spectral curves of N $$ \mathcal{N} $$ = 1 theories of class S k $$ {\mathcal{S}}_k $$

Non-perturbative aspects of N = 2 $$ \mathcal{N}=2 $$ supersymmetric gauge theories of class S $$ \mathcal{S} $$ are deeply encoded in the algebra of functions on the moduli space ℳ flat $$ {\mathrm{\mathcal{M}}}_{\mathrm{flat}} $$ of flat SL( N )- connections on Riemann surfaces. Expectation values of Wilson and ’t Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on ℳ flat $$ {\mathrm{\mathcal{M}}}_{\mathrm{flat}} $$ . Via the decomposition of UV line operators into IR line operators, we determine their noncommutative algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein algebra studied in the context of Chern-Simons theory. Another realization of the skein algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class S $$ \mathcal{S} $$ theories.

Maxime Gabella

Jörg Teschner

Line operators in theories of class S $$ \mathcal{S} $$ , quantized moduli space of flat connections, and Toda field theory