arXiv subjects

Roberta A. Iseppi

Publications and source records attributed to Roberta A. Iseppi.

3 recordsLinked to original sources

arXiv2019

The BRST cohomology and a generalized Lie algebra cohomology: analysis of a matrix model

This article is devoted to the analysis of the gauge-fixed BRST cohomology complex for a matrix model endowed with a $U(2)$-gauge symmetry. After a brief introduction on the BV construction and the gauge-fixing procedure in the setting of finite-dimensional gauge theories, we apply these constructions to the model, with the purpose of explicitly determining and computing the corresponding gauge-fixed BRST cohomology groups. In the second part of this article, we introduce a notion of generalized Lie algebra cohomology, which allows the gauge-fixed BRST cohomology complex for a new description, able to detect a double complex structure.

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arXiv2016

The BV formalism: theory and application to a matrix model

We review the BV formalism in the context of $0$-dimensional gauge theories. For a gauge theory $(X_{0}, S_{0})$ with an affine configuration space $X_{0}$, we describe an algorithm to construct a corresponding extended theory $(\tilde{X}, \tilde{S})$, obtained by introducing ghost and anti-ghost fields, with $\tilde{S}$ a solution of the classical master equation in $\mathcal{O}_{\tilde{X}}$. This construction is the first step to define the (gauge-fixed) BRST cohomology complex associated to $(\tilde{X}, \tilde{S})$, which encodes many interesting information on the initial gauge theory $(X_{0}, S_{0})$. The second part of this article is devoted to the application of this method to a matrix model endowed with a $U(2)$-gauge symmetry, explicitly determining the corresponding $\tilde{X}$ and the general solution $\tilde{S}$ of the classical master equation for the model.

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arXiv2016

Noncommutative geometry and the BV formalism: application to a matrix model

We analyze a U(2)-matrix model derived from a finite spectral triple. By applying the BV formalism, we find a general solution to the classical master equation. To describe the BV formalism in the context of noncommutative geometry, we define two finite spectral triples: the BV spectral triple and the BV auxiliary spectral triple. These are constructed from the gauge fields, ghost fields and anti-fields that enter the BV construction. We show that their fermionic actions add up precisely to the BV action. This approach allows for a geometric description of the ghost fields and their properties in terms of the BV spectral triple.

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