Quiver W-algebras

For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds–Kac–Moody Lie algebras, their quantum affinizations and associated W-algebras.     

Quiver elliptic W-algebras

We define elliptic generalization of W-algebras associated with arbitrary quiver using our construction (Kimura and Pestun in Quiver W-algebras, 2015. arXiv:1512.08533 [hep-th]) with six-dimensional gauge theory.     

Yangians and finite W-algebras

Using an algebra morphism between Yangians and some finite W-algebras, we determine the (product of) finite dimensional representations of the latters. This demonstrates a correspondence between evaluation representations of Yangians and Miura representations of W-algebras.     

W-algebras for generalized Toda theories

The generalized Toda theories obtained in a previous paper by the conformal reduction of WZNW theories possess a new class ofW-algebras, namely the algebras of gauge-invariant polynomials of the reduced theories. An algorithm for the construction of base-elements for theW-algebras of all such generalized Toda theories is found, and theW-algebras for the maximalSL(N,R) generalized Toda theories are constructed explicitly, the primary field basis being identified.     

Higher-rank isomonodromic deformations and W-algebras

Letters in Mathematical Physics - We construct the general solution of a class of Fuchsian systems of rank N as well as the associated isomonodromic tau functions in terms of semi-degenerate...     

q-deformed W-algebras and elliptic algebras

The elliptic algebra A _q,p {sl}(N _c) at the critical level c = –N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the W _N algebra, are constructed. The operators t(z) also close an exchange algebra when (–p ^1/2) ^NM = q ^–c–N for M . It becomes Abelian when in addition p = q ^Nh where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W _N algebras depending on the parity of h, characterizing the exchange structures at p q ^Nh as new W _q,p(sl(N)) algebras.     

A quiver quantum group

We construct quantum groups at a root of unity and we describe their monoidal module category using techniques from the representation theory of finite dimensional associative algebras.Supported by the FNSRS (Swiss National Foundation)     

Super-Toda theories and W-algebras from superspace Wess-Zumino-Witten models

Using a superspace approach, it is proved that aN=1 Super-Toda theory can be seen as a constrained WZW model based on a supergroup. The gauge transformations which survive the constraints are then usedà la Drinfeld Sokolov to determine explicity the super-W algebra underlying this theory. The conformal spin content of any such super-Walgebra is provided in the general case.URA 14-36 du CNRS, associée à l'E.N.S. de Lyon, et au L.A.P.P.     

Twisted quiver bundles over almost complex manifolds

In this paper, we study twisted quiver bundle over general almost complex manifolds. A twisted quiver bundle is a set of J-holomorphic vector bundles over an almost complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of J-holomorphic vector bundles, labelled by the arrows. We prove a Hitchin–Kobayashi correspondence for twisted quiver bundles over a compact almost Hermitian regularized manifold, relating the existence of solutions to certain gauge equations to an appropriate notion of stability for the corresponding quivers. This result can be seen as a generalization of that in [2], [9].     

Equivariant dimensional reduction and quiver gauge theories

We review recent applications of equivariant dimensional reduction techniques to the construction of Yang-Mills–Higgs–Dirac theories with dynamical mass generation and exactly massless chiral fermions.     

Integrating over quiver variety and BPS/CFT correspondence

Letters in Mathematical Physics - We show the vertex operator formalism for the quiver gauge theory partition function and the qq-character of the highest weight module on quiver, both associated...     

New example of infinite family of quiver gauge theories

We construct a new infinite family of quiver gauge theories which blow down to the Xp,q$X^{p,q}$ quiver gauge theories found by Hanany, Kazakopoulos and Wecht. This family includes a quiver gauge theory for the third del Pezzo surface. We show, using Z-minimization, that these theories generically have irrational R-charges. The AdS/CFT correspondence implies that the dual geometries are irregular toric Sasaki–Einstein manifolds, although we do not know the explicit metrics.