Maxim Zabzine

• Equivariant Batalin-Vilkovisky formalism

  2019-07-19

  arXiv:1907.07995
  
  by: Bonechi, Francesco (INFN, Florence) et al.
  
  Abstract:
  We study an equivariant extension of the Batalin-Vilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation, and we apply it to the natural equivariant extension of AKSZ solutions of the classical master equation (CME). As examples of the construction, we recover the equivariant extension of supersymmetric Yang-Mills in 2d and of Donaldson-Witten theory....

• Transversally Elliptic Complex and Cohomological Field Theory

  2019-04-30

  arXiv:1904.12782
  UUITP-16-19
  
  by: Festuccia, Guido (Uppsala U.) et al.
  
  Abstract:
  This work is a continuation of our previous paper arXiv:1812.06473 where we have constructed ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. In this work we expand on the mathematical aspects of the theory, with a particular focus on its nature as a cohomological field theory. The well-known Donaldson-Witten theory is a twisted version of ${\cal N}=2$ SYM and can also be constructed using the Atiy...

• Twisting with a Flip (the Art of Pestunization)

  2018-12-18

  arXiv:1812.06473
  
  by: Festuccia, Guido (Uppsala U.) et al.
  
  Abstract:
  We construct ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions to the partition function, and that this is compatible with supersymmetry. The equivariant Donaldson-Witten theory is a special case of our construction. We present a unified treatment of Pestun's calculation on $S^4$ and equivariant Donaldson-Witten...

• Solving q-Virasoro constraints

  2018-10-02

  arXiv:1810.00761
  
  by: Lodin, Rebecca (Uppsala U.) et al.
  
  Abstract:
  We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative insertions for beta-ensembles. From free-field point of view the models considered have zero momentum of the highest weight, which leads to an extra constraint T_{-1} Z = 0. We then show how to solve these q-Virasoro constraints recursively and comme...

• 3d Mirror Symmetry from S-duality

  2018-09-05

  arXiv:1809.00736
  UUITP-37/18
  Phys.Rev. D98 (2018) 126002
  
  by: Nieri, Fabrizio (Uppsala U.) et al.
  
  Abstract:
  We consider type IIB SL(2,Z) symmetry to relate the partition functions of different 5d supersymmetric Abelian linear quiver Yang-Mills theories in the Ω-background and squashed S5 background. By Higgsing S-dual theories, we extract new and old 3d mirror pairs. Generically, the Higgsing procedure yields 3d defects on intersecting spaces, and we derive new hyperbolic integral identities expressing the equivalence of the squashed S3 par...

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