Related papers: The ODE/IM Correspondence between $C(2)^{(2)}$-typ…

We consider the $4d$ $\mathcal{N}=2$ superconformal quiver gauge theory obtained by a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super Yang-Mills (SYM). By exploiting supersymmetric localization, we study the integrated correlator of two…

We continue to investigate the relationship between the infrared physics of N=2 supersymmetric gauge theories in four dimensions and various integrable models such as Gaudin, Calogero-Moser and quantum spin chains. We prove interesting…

Sigma models on coset superspaces, such as odd dimensional superspheres, play an important role in physics and in particular the AdS/CFT correspondence. In this work we apply recent general results on the spectrum of coset space models and…

The ODE/IM correspondence is an exact link between classical and quantum integrable models. The primary purpose of this work is to show that it remains valid after $\mathrm{T}\bar{\mathrm{T}}$ perturbation on both sides of the…

This paper investigates a reverse space-time higher-order modified self-steepening nonlinear Schr\"odinger equation, which distinguishes its standard local counterparts through the reverse space-time symmetry. The integrability of this…

We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above…

We build the general conformally invariant linear wave operator for a free, symmetric, second-rank tensor field in a d-dimensional ($d\geqslant 2$) metric manifold, and explicit the special case of maximally symmetric spaces. Under the…

We review the role of integrability in the planar spectral problem of four-dimensional superconformal gauge theories besides N=4 SYM. The cases considered include the Leigh-Strassler marginal deformations of N=4 SYM, quiver theories which…

We consider mixed four-point correlators of 1/2-BPS operators $\mathcal{O}_{k}$ in the maximally supersymmetric CFTs, i.e. the 3d $\mathcal{N}=8$, 4d $\mathcal{N}=4$, and 6d $\mathcal{N}=(2,0)$ theories. In arXiv:hep-th/0405180, Dolan,…

We consider the ODE/IM correspondence for the value $c=-2$ of the Virasoro central charge (free-fermion point) and the associated quantum KdV model $-$ the quantization of the second hamiltonian structure of the classical periodic KdV…

We study supersymmetric $AdS_4\times \Sigma_2$ and $AdS_3\times \Sigma_3$ solutions in half-maximal gauged supergravity in six dimensions with $SU(2)_R\times SU(2)$ gauge group. The gauged supergravity is obtained by coupling three vector…

We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of…

We review the quiver matrix model (the ITEP model) in the light of the recent progress on 2d-4d connection of conformal field theories, in particular, on the relation between Toda field theories and a class of quiver superconformal gauge…

We use the group-theoretic interpretation of the AdS/CFT correspondence which we proposed earlier in order to lift intertwining operators acting between boundary conformal representations to intertwining operators acting between bulk…

A recently proposed correspondence between 4-dimensional N=2 SUSY SU(k) gauge theories on R^4/Z_m and SU(k) Toda-like theories with Z_m parafermionic symmetry is used to construct four-point N=1 super Liouville conformal block, which…

We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…

We explore type II supersymmetric double field theory in superspace. The double supervielbein is an element of the orthosymplectic group OSp(10,10|64), which also governs the structure of generalized superdiffeomorphisms. Unlike bosonic…

Symmetries of the periodic Toda lattice are expresssed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Jacobi matrices. Using these symmetries, the phase space of the lattice…

We show that there is a family of two-dimensional $(0,2)$ SCFTs associated with twisted compactifications of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central…

There are two major ways of constructing 4d $\mathcal{N}=2$ superconformal field theories (SCFTs): the first one is putting a 6d $(2,0)$ theory on a punctured Riemann surface (class-S theory), and the second one is putting type IIB string…