We report a novel BPS jumping phenomenon of 5d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetric gauge theories whose brane configuration is equipped with an O7-plane. The study of the relation between O7+-plane and O7 − -plane reveals that such BPS jumps take place when the Higgsing is triggered near the O7-plane upon a particular parameter tuning of the theories. We propose two types of gauge theories whose BPS spectra jump. One is the SU(2N + 8) gauge theory with a symmetric hypermultiplet converted to the SU(2N) gauge theory with an antisymmetric hypermultiplet. The other is pure SO(2N + 8) gauge theory jumping to pure Sp(N) gauge theory. We explicitly confirm our proposal through the (un)refined instanton partition functions. Furthermore, we discuss feasible generalizations involving an Op-plane for supersymmetric gauge theories of eight supercharges in four and three dimensions (p = 6, 5 respectively).

China

Sung-Soo Kim

Xiaobin Li

Satoshi Nawata

Futoshi Yagi

Freezing and BPS jumping

We study two-dimensional <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math> and <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>4</mn><mo>)</mo></math> theories derived from compactifying class <math><mi>S</mi></math> theories on <math><msup><mi>S</mi><mn>2</mn></msup></math> with a topological twist. We present concise expressions for the elliptic genera of both classes of theories, revealing the topological quantum field theory structure on Riemann surfaces <math><msub><mi>C</mi><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub></math>. Furthermore, our study highlights the relationship between the left-moving sector of the (0,2) theory and the chiral algebra of the four-dimensional <math><mi>N</mi><mo>=</mo><mn>2</mn></math> theory. Notably, we propose that the (0,2) elliptic genus of a theory of this class can be expressed as a linear combination of characters of the corresponding chiral algebra.

Yiwen Pan

Jiahao Zheng

Class <math><mi>S</mi></math> theories on <math><msup><mi>S</mi><mn>2</mn></msup></math>

The qq-characters are powerful tools to reveal symmetries and integrabilities of Seiberg-Witten theories. The goal of this paper is to provide analytic expressions of qq-characters based on Young diagrams in 5d 𝒩 = 1 pure Yang-Mills theories with BCD-type gauge groups, by focusing on the unrefined limit. Using these expressions, we investigate the relationships among qq-characters of classical gauge groups. For SO(n) gauge groups, we construct a quantum-toroidal-like algebra via the Ward-identity approach, which allows us to derive the qq-characters.

Kilar Zhang

Rui-Dong Zhu

ABCD of qq-characters

We present the unrefined instanton partition functions of various 5d gauge theories with matter beyond the fundamental representation as sums over Young diagrams. By using these explicit expressions, we verify a range of identities among the instanton partition functions predicted by Higgsing procedures of fivebrane web diagrams and representation theory.

Yanyan Chen

Jiaqun Jiang

France

Yilu Shao

Instantons on Young diagrams with matters

Supersymmetric Sp(k) quantum chromodynamics with 8 supercharges in space-time dimensions 3 to 6 can be realised by two different Type II brane configurations in the presence of orientifolds. Consequently, two types of magnetic quivers describe the Higgs branch of the Sp(k) SQCD theory. This is a salient example of a general phenomenon: a given hyper-Kähler Higgs branch may admit several magnetic quiver constructions. It is then natural to wonder if these different magnetic quivers, which are described by 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 theories, are dual theories. In this work, the unitary and orthosymplectic magnetic quiver theories are subjected to a variety of tests, providing evidence that they are IR dual to each other. For this, sphere partition function and supersymmetric indices are compared. Also, we study half BPS line defects and find interesting regularities from the viewpoints of exact results, brane configurations, and 1-form symmetry.

Marcus Sperling

Hao Wang

United Kingdom

Zhenghao Zhong

Magnetic quivers and line defects — On a duality between 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 unitary and orthosymplectic quivers

We present closed-form expressions of unrefined instanton partition functions for gauge groups of type BCD as sums over Young diagrams. For SO(n) gauge groups, we provide a fivebrane web picture of our formula based on the vertex-operator formalism of the topological vertex with a new type called O-vertex for an O5-plane.

Instanton counting and O-vertex

By studying the infrared fixed point of an <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math> Landau-Ginzburg model, we find an example of modular invariant partition function beyond the ADE classification. This stems from the fact that a part of the left-moving sector is a new conformal field theory which is a variant of the parafermion model with level twenty-five.

Jirui Guo

United States

Runkai Tao

Hao Derrick Zhang

New conformal field theory from <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mtext> </mtext><mn>2</mn><mo>)</mo></math> Landau-Ginzburg model

This paper provides both a detailed study of color-dependence of link homologies, as realized in physics as certain spaces of BPS states, and a broad study of the behavior of BPS states in general. We consider how the spectrum of BPS states varies as continuous parameters of a theory are perturbed. This question can be posed in a wide variety of physical contexts, and we answer it by proposing that the relationship between unperturbed and perturbed BPS spectra is described by a spectral sequence. These general considerations unify previous applications of spectral sequence techniques to physics, and explain from a physical standpoint the appearance of many spectral sequences relating various link homology theories to one another. We also study structural properties of colored HOMFLY homology for links and evaluate Poincaré polynomials in numerous examples. Among these structural properties is a novel “sliding” property, which can be explained by using (refined) modular S -matrix. This leads to the identification of modular transformations in Chern-Simons theory and 3d N = 2 $$ \mathcal{N}=2 $$ theory via the 3d/3d correspondence. Lastly, we introduce the notion of associated varieties as classical limits of recursion relations of colored superpolynomials of links, and study their properties.

Germany

Sergei Gukov

Denmark

Ingmar Saberi

Serbia

Portugal

Marko Stošić

Poland

Piotr Sułkowski

Sequencing BPS spectra

We study the structural properties of colored Kauffman homologies of knots. Quadruple-gradings play an essential role in revealing the differential structure of colored Kauffman homology. Using the differential structure, the Kauffman homologies carrying the symmetric tensor products of the vector representation for the trefoil and the figure-eight are determined. In addition, making use of relations from representation theory, we also obtain the HOMFLY homologies colored by rectangular Young tableaux with two rows for these knots. Furthermore, the notion of super- A -polynomials is extended in order to encompass two-parameter deformations of PSL(2, ℂ) character varieties.