The BRST operator of quantum symmetries: The quantum analogs of Donaldson invariants

1997 ◽  
Vol 38 (9) ◽  
pp. 4462-4473 ◽  
Author(s):  
A. B. Hammou ◽  
M. Lagraa
Keyword(s):  
Brst Operator ◽  
Quantum Symmetries ◽  
Donaldson Invariants

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

scholarly journals Mocking the u-plane integral

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Georgios Korpas ◽  
Jan Manschot ◽  
Gregory W. Moore ◽  
Iurii Nidaiev
Keyword(s):  
Asymptotic Behavior ◽  
Gauge Theory ◽  
Entire Function ◽  
Gauge Group ◽  
Strong Coupling ◽  
Modular Forms ◽  
Correlation Functions ◽  
Coulomb Branch ◽  
Mock Modular Forms ◽  
Donaldson Invariants

AbstractThe u-plane integral is the contribution of the Coulomb branch to correlation functions of $${\mathcal {N}}=2$$ N = 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group $$\mathrm{SU}(2)$$ SU ( 2 ) , for an arbitrary four-manifold with $$(b_1,b_2^+)=(0,1)$$ ( b 1 , b 2 + ) = ( 0 , 1 ) . The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

scholarly journals BRST operator for superconformal algebras with quadratic nonlinearity

1994 ◽  
Vol 326 (3-4) ◽  
pp. 243-250 ◽  
Author(s):  
Z. Khviengia ◽  
E. Sezgin
Keyword(s):  
Quadratic Nonlinearity ◽  
Brst Operator

scholarly journals On the BRST operator structure of the N = 2 string

1993 ◽  
Vol 400 (1-3) ◽  
pp. 145-160 ◽  
Author(s):  
Amit Giveon ◽  
Martin Roček
Keyword(s):  
Brst Operator ◽  
Operator Structure

ONE-LOOP VACUUM ENERGY AT THE TACHYON VACUUM

2013 ◽  
Vol 21 ◽  
pp. 157-158
Author(s):  
SHOKO INATOMI
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
String Field Theory ◽  
Vacuum Energy ◽  
Open String ◽  
Brst Operator ◽  
Identity Based ◽  
Homotopy Operators

We consider one-loop vacuum energy at the tachyon vacuum in cubic bosonic open string field theory. The BRST operator Ql in the theory around an identity-based solution is believed to represent a kinetic operator at the tachyon vacuum. Using homotopy operators for Ql, we find that one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances. This result can be interpreted as support for the annihilation of D-branes at the tachyon vacuum even in the quantum theory.

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