arXiv subjects

Darren T. Grasso

Publications and source records attributed to Darren T. Grasso.

5 recordsLinked to original sources

arXiv2026

Heat kernel approach to the one-loop effective action for nonlinear electrodynamics

We develop a heat kernel method to compute the one-loop effective action for a general class of nonlinear electrodynamic (NLED) theories in four dimensional Minkowski spacetime. Working in the background field formalism, we extract the logarithmically divergent part of the effective action, the so-called induced action, corresponding to the DeWitt $a_2$ coefficient of the heat kernel. In NLED, quantisation yields non-minimal differential operators, for which standard heat kernel techniques are not immediately applicable. Considering the weak-field regime, we calculate the $a_0$, $a_1$ and $a_2$ contributions to leading order in the background electromagnetic field strength. Finally, we consider conformal NLED theories and compute the $a_0$ contribution to all orders. For this class, we comment on the role of causality being necessary and sufficient for the convergence of the exact $a_1$ and $a_2$ contributions.

hep-th↗

arXiv2023

Effective actions in supersymmetric gauge theories: heat kernels for non-minimal operators

We study the quantum dynamics of a system of $n$ Abelian ${\cal N}=1$ vector multiplets coupled to $\frac 12 n(n+1)$ chiral multiplets which parametrise the Hermitian symmetric space $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. In the presence of supergravity, this model is super-Weyl invariant and possesses the maximal non-compact duality group $\mathsf{Sp}(2n, {\mathbb R})$ at the classical level. These symmetries should be respected by the logarithmically divergent term (the ``induced action'') of the effective action obtained by integrating out the vector multiplets. In computing the effective action, one has to deal with non-minimal operators for which the known heat kernel techniques are not directly applicable, even in flat (super)space. In this paper we develop a method to compute the induced action in Minkowski superspace. The induced action is derived in closed form and has a simple structure. It is a higher-derivative superconformal sigma model on $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. The obtained ${\cal N}=1$ results are generalised to the case of ${\cal N}=2$ local supersymmetry: a system of $n$ Abelian ${\cal N}=2$ vector multiplets coupled to ${\cal N}=2$ chiral multiplets $X^I$ parametrising $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. The induced action is shown to be proportional to $ \int {\rm d}^4x {\rm d}^4 θ{\rm d}^4 \bar θ\, E \, {\mathfrak K}(X, \bar X )$, where ${\mathfrak K}(X, \bar X )$ is the Kähler potential for $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. We also apply our method to compute DeWitt's $a_2 $ coefficients in some non-supersymmetric theories with non-minimal operators.

hep-th↗

arXiv2023

Weyl invariance, non-compact duality and conformal higher-derivative sigma models

We study a system of $n$ Abelian vector fields coupled to $\frac 12 n(n+1)$ complex scalars parametrising the Hermitian symmetric space $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. This model is Weyl invariant and possesses the maximal non-compact duality group $\mathsf{Sp}(2n, {\mathbb R})$. Although both symmetries are anomalous in the quantum theory, they should be respected by the logarithmic divergent term (the ``induced action'') of the effective action obtained by integrating out the vector fields. We compute this induced action and demonstrate its Weyl and $\mathsf{Sp}(2n, {\mathbb R})$ invariance. The resulting conformal higher-derivative $σ$-model on $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$ is generalised to the cases where the fields take their values in (i) an arbitrary Kähler space; and (ii) an arbitrary Riemannian manifold. In both cases, the $σ$-model Lagrangian generates a Weyl anomaly satisfying the Wess-Zumino consistency condition.

hep-th↗

arXiv2004

Higher order contributions to the effective action of N=2 super Yang-Mills

We apply heat kernel techniques in N=1 superspace to compute the one-loop effective action to order $F^5$ for chiral superfields coupled to a non-Abelian super Yang-Mills background. The results, when combined with those of hep-th/0210146, yield the one-loop effective action to order $F^5$ for any N=2 super Yang-Mills theory coupled to matter hypermultiplets.

hep-th↗

arXiv2002

Higher order contributions to the effective action of N=4 super Yang-Mills

The one-loop low-energy effective action for non-Abelian N=4 supersymmetric Yang-Mills theory is computed to order $F^6$ by use of heat kernel techniques in N=1 superspace. At the component level, the $F^5$ terms are found to be consistent with the form of the non-Abelian Born-Infeld action computed to this order by superstring methods. The $F^6$ terms will be of importance for comparison with superstring calculations.

hep-th↗