Related papers: Wall crossing, string networks and quantum toroida…

The BPS state spectrum in four-dimensional gauge theories or string vacua with N=2 supersymmetries is well known to depend on the values of the parameters or moduli at spatial infinity. The BPS index is locally constant, but discontinuous…

Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…

We discuss a set of heterotic and type II string theory compactifications to 1+1 dimensions that are characterized by factorized internal worldsheet CFTs of the form $V_1\otimes \bar V_2$, where $V_1, V_2$ are self-dual (super) vertex…

Recently, new classes of infinite-dimensional algebras, quiver Yangian (QY) and shifted QY, were introduced, and they act on BPS states for non-compact toric Calabi-Yau threefolds. In particular, shifted QY acts on general subcrystals of…

I review my work together with Piljin Yi on the spectrum of BPS-saturated states in N = 2 supersymmetric Yang-Mills theories. In an M-theory description, such states are realized as certain two-brane configurations. We first show how the…

The quiver Yangian, an infinite-dimensional algebra introduced recently in arXiv:2003.08909, is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of quiver…

In this work, we uncover a collection of non invertible topological operators linked to the 0-, 2-, 4- and 6-form symmetries related to the type IIB superstring effective theory. By pinpointing the $\text{SL}(2,\mathbb{Z})$-covariant…

We consider the exact S-matrix governing the planar spectral problem for strings on $AdS_5\times S^5$ and $\mathcal N=4$ super Yang-Mills, and we show that it is invariant under a novel "boost" symmetry, which acts as a differentiation with…

Domain walls in supersymmetric Yang-Mills are BPS configurations which preserve two supercharges of the parent theory and so their tensions are known exactly. On the other hand, they have been described as D-branes for the confining string.…

We study the superstring theory on pp-wave background with NSNS-flux that is realized as the Penrose limit of AdS_3 x S^3 x M^4, where M^4 is T^4 or T^4/Z_2(~ K3). Quantizing this system in the covariant gauge, we explicitly construct the…

We show how the Riemann surface $\Sigma$ of $N=2$ Yang-Mills field theory arises in type II string compactifications on Calabi-Yau threefolds. The relevant local geometry is given by fibrations of ALE spaces. The $3$-branes that give rise…

We explore the physics of two-body decay of BPS states using semiclassical analysis to construct explicit solutions that illustrate the main features of wall crossing, for both ordinary and framed BPS states. In particular we recover the…

We explore the relationship between four-dimensional N=2 quantum field theories and their associated BPS quivers. For a wide class of theories including super-Yang-Mills theories, Argyres-Douglas models, and theories defined by M5-branes on…

The instanton partition functions of $\mathcal{N}=1$ 5d super Yang-Mills are built using elements of the representation theory of quantum $\mathcal{W}_{1+\infty}$ algebra: Gaiotto state, intertwiner, vertex operator. This algebra is also…

In this paper we present a discrete, non-perturbative formulation for type IIB string theory. Being a supersymmetric quiver matrix mechanics model in the framework of M(atrix) theory, it is a generalization of our previous proposal of…

This paper studies in great detail a family of supersymmetric Wilson loop operators in N=4 supersymmetric Yang-Mills theory we have recently found. For a generic curve on an S^3 in space-time the loops preserve two supercharges but we will…

We propose generating functions which encode the degeneracies and wall-crossing phenomena of $\mathcal{N}=2$ BPS structures. The generating functions have a representation-theoretic origin and are the analogs of the 1/4-BPS dyon counting…

We study the BPS spectrum of four-dimensional $\mathcal{N}=2$ superconformal field theory of Argyres-Douglas type, obtained via twisted compactification of six-dimensional $A_{N-1}$ $(2,0)$ theory on a sphere with an irregular puncture, by…

We construct and explore BPS states that preserve 1/4 of supersymmetry in N=4 Yang-Mills theories. Such states are also realized as three-pronged strings ending on D3-branes. We correct the electric part of the BPS equation and relate its…

We study supersymmetric open strings in type IIB $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed R-R and NS-NS fields. We focus on strings ending along a straight line at the boundary of $AdS_3$, which can be interpreted as line…