The Β-Function IN TOPOLOGICAL SIGMA MODELS

Birmingham, Danny; Rakowski, Mark

doi:10.1142/s0217732391000075

Cited by 34 publications

(92 citation statements)

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“…These operators {D + , D + µ , D + A } satisfy the following relations: 5) where Z commutes these operators…”

Section: N = Twisted Susy With Central Chargementioning

confidence: 99%

Vafa-Witten theory onN= 2 andN= 4 twisted superspace in four dimensions

Kato¹,

Miyake²

2009

J. High Energy Phys.

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We construct a new off-shell twisted hypermultiplet with a scalar and an anti-self-dual tensor superfields. Using the N = 2 twisted superspace formalism, we construct a Donaldson-Witten theory coupled to the hypermultiplet. We show that this action possesses the Vafa-Witten type N = 4 twisted supersymmetry at the on-shell level. We also reconstruct the action using a N = 4 twisted superconnection formalism.

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“…These operators {D + , D + µ , D + A } satisfy the following relations: 5) where Z commutes these operators…”

Section: N = Twisted Susy With Central Chargementioning

confidence: 99%

Vafa-Witten theory onN= 2 andN= 4 twisted superspace in four dimensions

Kato¹,

Miyake²

2009

J. High Energy Phys.

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“…In [1]- [4], it was shown that a certain vector supersymmetry algebra was powerful enough to supply a foundation for both cohomological gauge and gravity theories; the gauge theories could be based on a theory of global vector supersymmetry, while local vector supersymmetry was the essential ingredient for gravity. Although a formulation of cohomological gauge theory was already known [5], an equally satisfactory treatment of gravity was elusive, for various attempts see [6]- [16].…”

Section: Introductionmentioning

confidence: 99%

“…It was observed in [1] that the underlying algebra of cohomological gauge theory contained a global vector supersymmetry operator, in addition to the known BRST symmetry [5]. This led to an algebraic understanding of the descent equations de ning the observables, and indicated the generalization to a theory of cohomological gravity.…”

Section: Introductionmentioning

confidence: 99%

“…This led to an algebraic understanding of the descent equations de ning the observables, and indicated the generalization to a theory of cohomological gravity. By looking for realizations of a local vector supersymmetry algebra, a multiplet was obtained that was generic to all dimensions [2]. This multiplet does not contain an independent spin connection, and one should not regard this formulation as a \gauge theory" approach t o topological gravity.…”

Section: Introductionmentioning

confidence: 99%

“…This provides a uni ed picture for treating realizations of a global, or local, vector supersymmetry algebra. The basic multiplet and symmetries of cohomological gauge theory are shown to be encoded in this superspace formalism by a particular choice of covariant torsion and curvature constraints [1]. The generalization to gravity i s then presented, and the minimal multiplet and observables are obtained [2].…”

Section: Introductionmentioning

confidence: 99%

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The algebraic structure of cohomological field theory

Birmingham

Rakowski

1993

Journal of Geometry and Physics

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The algebraic foundation of cohomological eld theory is presented. It is shown that these theories are based upon realizations of an algebra which contains operators for both BRST and vector supersymmetry. Through a localization of this algebra, we construct a theory of cohomological gravity in arbitrary dimensions. The observables in the theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. A s such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach, di erent moduli spaces are obtained by i n troducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occurring di erential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum eld theory, and the discrete Regge calculus.

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Gravity from Lie Algebroid Morphisms

Strobl

2004

Communications in Mathematical Physics

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Inspired by the Poisson Sigma Model and its relation to 2d gravity, we consider models governing morphisms from T Σ to any Lie algebroid E, where Σ is regarded as d-dimensional spacetime manifold. We address the question of minimal conditions to be placed on a bilinear expression in the 1-form fields, S ij (X)AiAj , so as to permit an interpretation as a metric on Σ. This becomes a simple compatibility condition of the E-tensor S with the chosen Lie algebroid structure on E. For the standard Lie algebroid E = T M the additional structure is identified with a Riemannian foliation of M , in the Poisson case E = T * M with a sub-Riemannian structure which is Poisson invariant with respect to its annihilator bundle. (For integrable image of S, this means that the induced Riemannian leaves should be invariant with respect to all Hamiltonian vector fields of functions which are locally constant on this foliation). This provides a huge class of new gravity models in d dimensions, embedding known 2d and 3d models as particular examples.

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The Β-Function IN TOPOLOGICAL SIGMA MODELS

Abstract: The one-loop β-function is computed for topological sigma models. By gauge fixing the topological shift symmetry in the delta-function gauge, we find that the theory is finite with vanishing β-function. A similar result is shown to hold for supersymmetric quantum mechanics.

Cited by 34 publications

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Vafa-Witten theory onN= 2 andN= 4 twisted superspace in four dimensions

Vafa-Witten theory onN= 2 andN= 4 twisted superspace in four dimensions

The algebraic structure of cohomological field theory

Gravity from Lie Algebroid Morphisms

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