scholarly journals Penrose Transform on <i>D</i>-Modules, Moduli Spaces and Field Theory

2012 ◽  
Vol 02 (06) ◽  
pp. 379-390 ◽  
Author(s):  
Francisco Bulnes
Keyword(s):  
Field Theory ◽  
Moduli Spaces ◽  
Penrose Transform

scholarly journals Toward AGT for Parabolic Sheaves

2020 ◽  
Author(s):  
Andrei Neguţ
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conformal Field Theory ◽  
Moduli Spaces ◽  
Type A ◽  
Conformal Field ◽  
Toroidal Algebra ◽  
Agt Correspondence ◽  
K Theory ◽  
The Ideal

Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.

scholarly journals Instanton Moduli Spaces and Bases in Coset Conformal Field Theory

2012 ◽  
Vol 319 (1) ◽  
pp. 269-301 ◽  
Author(s):  
A. A. Belavin ◽  
M. A. Bershtein ◽  
B. L. Feigin ◽  
A. V. Litvinov ◽  
G. M. Tarnopolsky
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Moduli Spaces ◽  
Conformal Field

scholarly journals A polyfold proof of the Arnold conjecture

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Benjamin Filippenko ◽  
Katrin Wehrheim
Keyword(s):  
Field Theory ◽  
Moduli Spaces ◽  
Symplectic Manifolds ◽  
Joint Work ◽  
Pseudoholomorphic Curves ◽  
Countable Collection ◽  
Arnold Conjecture ◽  
Detailed Proof ◽  
Symplectic Field Theory

AbstractWe give a detailed proof of the homological Arnold conjecture for nondegenerate periodic Hamiltonians on general closed symplectic manifolds M via a direct Piunikhin–Salamon–Schwarz morphism. Our constructions are based on a coherent polyfold description for moduli spaces of pseudoholomorphic curves in a family of symplectic manifolds degenerating from $${{\mathbb {C}}{\mathbb {P}}}^1\times M$$ C P 1 × M to $${{\mathbb {C}}}^+ \times M$$ C + × M and $${{\mathbb {C}}}^-\times M$$ C - × M , as developed by Fish–Hofer–Wysocki–Zehnder as part of the Symplectic Field Theory package. To make the paper self-contained we include all polyfold assumptions, describe the coherent perturbation iteration in detail, and prove an abstract regularization theorem for moduli spaces with evaluation maps relative to a countable collection of submanifolds. The 2011 sketch of this proof was joint work with Peter Albers, Joel Fish.

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