arXiv subjects

Lorenzo Casarin

Publications and source records attributed to Lorenzo Casarin.

11 recordsLinked to original sources

arXiv2026

One-loop divergences for KK theories on $\mathrm{AdS}\times S$ spaces; a reanalysis of $\mathrm{AdS}_4 \times S^7\,\big/$ ABJM precision holography

We provide a systematic framework for computing the logarithmically divergent part of one-loop partition functions on product spaces $\mathrm{AdS}_{d_A} \times S^{d_S}$ of arbitrary dimension. By expanding the higher-dimensional kinetic operators in spherical harmonics, we reduce the ($d_A+d_S$)-dimensional spectral problem to an infinite tower of $d_A$-dimensional determinants, which are then represented via spectral $ζ$-function methods. We isolate the logarithmic divergences arising from the interplay between the individual AdS determinants and the infinite Kaluza-Klein sum, carefully accounting for the contributions of zero modes on the sphere that produce additional AdS determinants. We test this framework on different fields and apply it to the complete multiplet of 11-dimensional supergravity on $\mathrm{AdS}_4 \times S^7$. We recover in a 4d language the result of arXiv:1210.6057, namely that the only non-vanishing logarithmic divergence originates entirely from the 2-form AdS mode in the ghost sector, reproducing the well-known $\frac{1}{4}\log N$ correction to the ABJM free energy predicted by supersymmetric localization.

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arXiv2025

Conformal anomalies for (maximal) 6d conformal supergravity

We compute the conformal anomalies for 6d (2,0) conformal supergravity by direct calculation in component fields. The main novel results consist of the type-B anomaly coefficients for the gravitino and the 3-form, as well as their explicit quadratic action on some specific backgrounds. We also comment on the graviton contribution, whose Lagrangian is essentially given by the $\mathscr Q$-curvature. We confirm the expectation that, when coupling (2,0) conformal supergravity to 26 copies of the (2,0) tensor multiplet, the resulting theory is free of conformal anomalies. We also consider the conformal anomalies for its (1,0) truncation and confirm their relation with the chiral anomaly polynomial recently derived. For calculating the anomalies, we work with an Einstein on-shell background and make a factorised Ansatz for the operators governing the quadratic fluctuations. This reduces the calculation to evaluating heat-kernel coefficients of standard 2-derivative operators. We fix and check the Ansatz against the explicit evaluation of the component-field supergravity action in some cases.

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arXiv2025

Nicolai maps with four-fermion interactions

Nicolai maps offer an alternative description of supersymmetric theories via nonlinear and nonlocal transformations characterized by the so-called `free-action' and `determinant-matching' conditions. The latter expresses the equality of the Jacobian determinant of the transformation with the one obtained by integrating out the fermions, which so far have been considered only to quadratic terms. We argue that such a restriction is not substantial, as Nicolai maps can be constructed for arbitrary nonlinear sigma models, which feature four-fermion interactions. The fermionic effective one-loop action then gets generalized to higher loops and the perturbative tree expansion of such Nicolai maps receives quantum corrections in the form of fermion loop decorations. The `free-action condition' continues to hold for the classical map, but the `determinant-matching condition' is extended to an infinite hierarchy in fermion loop order. After general considerations for sigma models in four dimensions, we specialize to the case of $\mathbb{C}\mathrm{P}^N$ symmetric spaces and construct the associated Nicolai map. These sigma models admit a formulation with only quadratic fermions via an auxiliary vector field, which does not simplify our analysis.

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arXiv2025

Semiclassical quantization of M5 brane probes wrapped on $\textrm{AdS}_3\times S^3$ and defect anomalies

We consider two supersymmetric M5 brane probe solutions in $\textrm{AdS}_7 \times S^4$ and one in $\textrm{AdS}_4 \times S^7$ that all have the $\textrm{AdS}_3 \times S^3$ world-volume geometry. The values of the classical action of the first two M5 probes (with $S^3$ in $\textrm{AdS}_7$ or in $S^4$) are related to the leading $N^2$ parts in the anomaly b-coefficient in the (2,0) theory corresponding to a spherical surface defect in symmetric or antisymmetric $SU(N)$ representations. We present a detailed computation of the corresponding one-loop M5 brane partition functions finding that they vanish (in a particular regularization). This implies the vanishing of the order $N^0$ part in the b-anomaly coefficients, in agreement with earlier predictions for their exact values. It remains, however, a puzzle of how to reproduce the non-vanishing order $N$ terms in these coefficients within the semiclassical M5-brane probe setup.

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arXiv2024

Conformal `anomalies' and renormalized stress-tensor correlators for non-conformal theories

We analyse the proposal of defining the Weyl anomaly for classically non-conformal theories as $g^{mn} \langle T_{mn}\rangle - \langle g^{mn} T_{mn} \rangle$, originally put forward by M. Duff, in the case of a scalar field with quartic self-interaction in 4d. We work in the context of dimensional regularization in curved background to two-loops (first order in the coupling). We review the original regularized but not renormalized prescription and its ambiguities; we argue that it cannot be extended to the interacting theory as it fails to provide a finite result. We then propose an alternative prescription via renormalized expectation values. At one-loop our candidate reproduces the local heat kernel result, while its extension to interacting theories contains non-local contributions.

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arXiv2023

Conformal anomalies in 6d 4-derivative theories: a heat-kernel analysis

We compute the conformal anomalies for some higher-derivative (non-unitary) 6d Weyl invariant theories using the heat-kernel expansion in the background-field method. To this aim we obtain the general expression for the Seeley-DeWitt coefficient $b_6$ for four-derivative differential operators with background curved geometry and gauge fields, which was known only in flat space so far. We consider four-derivative scalars and abelian vectors as well as three-derivative fermions, confirming the result of the literature obtained via indirect methods. We generalise the vector case by including the curvature coupling $FF \mathrm{Weyl}$.

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arXiv2022

ANEC on stress-tensor states in perturbative $λϕ^4$ theory

We evaluate the Average Null Energy Condition (ANEC) on momentum eigenstates generated by the stress tensor in perturbative $λ\, ϕ^4$ and general spacetime dimension. We first compute the norm of the stress-tensor state at second order in $λ$; as a by-product of the derivation we obtain the full expression for the stress tensor 2-point function at this order. We then compute the ANEC expectation value to first order in $λ$, which also depends on the coupling of the stress-tensor improvement term $ξ$. We study the bounds on these couplings that follow from the ANEC and unitarity at first order in perturbation theory. These bounds are stronger than unitarity in some regions of coupling space.

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arXiv2021

ANEC in $λ\, ϕ^4$ theory

Motivated by the goal of applying the average null energy condition (ANEC) to renormalisation group flows, we calculate in $λϕ^4$ theory the expectation value of the ANEC operator in a particular scalar state perturbatively up to third order in the quartic coupling and verify the expected CFT answer. The work provides the technical tools for studying the expectation value of the ANEC operator in more interesting states, for example tensorial states relevant to the Hofman-Maldacena collider bounds, away from critical points.

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arXiv2019

One-loop beta-functions in 4-derivative gauge theory in 6 dimensions

A classically scale-invariant 6d analog of the 4d Yang-Mills theory is the 4-derivative $ (\nabla F)^2 + F^3$ gauge theory with two independent couplings. Motivated by a search for a perturbatively conformal but possibly non-unitary 6d models we compute the one-loop $β$-functions in this theory. A systematic way of doing this using the background field method requires the expression for the $b_6$ Seeley-DeWitt coefficient for a generic 4-derivative operator. It was previously unknown and we derive it here. As an application, we also compute the one-loop $β$-function in the (1,0) supersymmetric $ (\nabla F)^2$ 6d gauge theory constructed in hep-th/0505082.

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arXiv2018

Conformal Anomaly for Non-Conformal Scalar Fields

We give a general definition of the conformal anomaly for theories that are not classically Weyl invariant and show that this definition yields a quantity that is both finite and local. As an example we study the conformal anomaly for a non-minimally coupled massless scalar and show that our definition coincides with results obtained using the heat kernel method.

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arXiv2017

On higher-derivative gauge theories

In this work we study the main properties and the one-loop renormalization of a Yang-Mills theory in which the kinetic term contains also a fourth-order differential operator; in particular, we add to the Yang-Mills Lagrangian the most general contribution of mass dimension six, weighted with a dimensionful parameter. This model is renormalizable; in the literature two values for the beta function for the gauge coupling have been reported, one obtained using the heat kernel approach and one with Feynman diagrams. In this work we repeat the computation using heat kernel techniques confirming the latter result. We also considered coupling with matter. We then study the supersymmetric extension of the model; this is a nontrivial task because of the complicate structure of the higher-derivative term. Some partial results were known, but a computation of the beta functions for the full supersymmetric non-Abelian higher-derivative gauge theory was missing. We make use of the (unextended) supersymmetric higher-derivative Lagrangian density for the Yang-Mills field in six spacetime dimensions derived in arXiv:hep-th/0505082; by dimensional reduction we obtain the N=1 and N=2 supersymmetric higher-derivative super-Yang-Mills Lagrangian in four spacetime dimensions, whose beta function we evaluate using heat kernels. We also deduce the beta function for N=4 supersymmetry.

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