Dmitri Vassilevich

Computing the vacuum expectation of a fermion number operator on a soliton background is often challenging. A recent proposal in [1] simplifies this task by considering the soliton in a bounded region and relating the η invariant, and thus the fermion number, to a specific heat kernel coefficient and to contributions from the edge states. We test this method in a system of charged fermions living on an Abrikosov-Nielsen-Olesen vortex background. We show that the resulting η invariant does not depend on boundary conditions (within a certain class), thereby supporting the validity of the method. Our analysis reveals a nontrivial feature for the fermionic spectrum in the vortex-induced Higgs phase. As a by-product, we also find that for a vortex living on a disk, the edge states carry a fractional charge.

In this paper, we consider a Carroll magnetic limit of a one-loop scalar effective action. We work on general static backgrounds and compute both divergent and finite parts of the effective action in this limit. We show that the divergent part can be removed by adding local counterterms. The finite part is related to an effective action in a lower dimensional theory which however does not coincide in general with the one obtained by a Carroll limit in the classical counterpart. Published by the American Physical Society 2025

A bstract: There exists a long-standing debate regarding the torsion contribution to the 4d chiral anomaly of a Dirac fermion. Central to this debate is the Nieh-Yan anomaly, which has been considered ill-defined and a regularization artifact. Using a heat-kernel approach, we examine the relationship between the Dirac operator index, the Nieh-Yan invariant and the torsional anomaly. We show the Nieh-Yan invariant vanishes on spacetimes without boundaries, if the Dirac index is well-defined. In the known examples of non-vanishing Nieh-Yan invariant on manifolds without boundaries, the heat kernel expansion breaks down, making the index ill-defined. Finally, for finite boundaries we identify several finite bulk and boundary anomaly terms, alongside bulk and boundary Nieh-Yan terms. We construct explicit counterterms that cancel the Nieh-Yan terms and argue that the boundary terms give rise to a torsional anomalous Hall effect. Our results emphasize the importance of renormalization conditions, as these can affect the non-thermal Nieh-Yan anomaly coefficients. In addition, we demonstrate that anomalous torsional transport may arise even without relying on the Nieh-Yan invariant.

Carroll black holes with an associated Carroll temperature were introduced recently. So far, it is unclear if they exhibit a Hawking-like effect. To solve this, we study scalar fields on Carroll black hole backgrounds. Inspired by anomaly methods, we derive a Hawking-like energy-momentum tensor compatible with the Carroll temperature and the Stefan-Boltzmann law. Key steps in our derivation are the finiteness of energy at the Carroll extremal surface and compatibility with the Carroll-Ward identities, thereby eliminating, respectively, the Carroll analogs of the Boulware and Unruh vacua. Published by the American Physical Society 2024

Carroll black holes with an associated Carroll temperature were introduced recently. So far, it is unclear if they exhibit a Hawking-like effect. To solve this, we study scalar fields on Carroll black hole backgrounds. Inspired by anomaly methods, we derive a Hawking-like energy-momentum tensor compatible with the Carroll temperature and the Stefan-Boltzmann law. Key steps in our derivation are the finiteness of energy at the Carroll extremal surface and compatibility with the Carroll Ward identities, thereby eliminating, respectively, the Carroll-analogs of the Boulware and Unruh vacua.

We explicitly construct an L$_\infty$ algebra that defines U$_{\star}(1)$ gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as L$_\infty$ modules. Some possibilities for including P$_\infty$ algebras are also discussed.

We explicitly construct an L ∞ algebra that defines U ⋆ ( 1 ) gauge transformations on a space with an arbitrary noncommutative and even nonassociative star product. Matter fields are naturally incorporated in this scheme as L ∞ modules. Some possibilities for including P ∞ algebras are also discussed.