We introduce generalisations of von Neumann entanglement entropy that are invariant with respect to certain scale transformations. These constructions are based on the Unit-Invariant Singular Value Decomposition (UISVD) in its left-, right-, and bi-invariant incarnations, which are variations of the standard Singular Value Decomposition (SVD) that remain invariant under the corresponding class of diagonal transformations. These measures are naturally defined for non-Hermitian or rectangular operators and remain useful when the input and output spaces possess different dimensions or metric weights. We apply the UISVD entropy and discuss its advantages in the physically interesting framework of Biorthogonal Quantum Mechanics, whose important aspect is indeed the behaviour under scale transformations. Further, we illustrate features of UISVD-based entropies in other well-known setups, from simple quantum mechanical bipartite states to random matrices relevant to quantum chaos and holography, and in the context of Chern-Simons theory. In all cases, the UISVD yields stable, physically meaningful entropic spectra that are invariant under rescalings and normalisations.

Japan

Poland

Sweden

Paweł Caputa

Abhigyan Saha

Piotr Sułkowski

Generalised entanglement entropies from Unit-Invariant Singular Value Decomposition

Generalised spin structures are necessary for placing fermions on manifolds that do not admit a standard spin structure. This is especially relevant in a dimensional reduction on such a manifold, which can then be compensated by using fermions that are appropriately charged under some Maxwell or Yang-Mills field defined on the internal manifold. A well known example in the physics literature is $$ {\mathbbm{CP}}^2 $$ , which has four real dimensions and is the coset SU(3)/U(2). In this paper we focus on a five-dimensional coset space, namely the Wu manifold SU(3)/SO(3) , where SO(3) is maximal in SU(3). Intriguingly, the Wu manifold does not admit a spin structure or spin structure, it does admit a spin structure. We provide a physical interpretation of the spin structure by considering spinors that are coupled to an SO(3) Yang-Mills field defined on the Wu manifold, but which carry half-integer “isospin,” thereby canceling the minus sign in the holonomy for uncharged spinors that provides the original obstruction to an ordinary spin structure. We also construct a gauge-covariantly constant spinor in the Wu manifold, and we show how this can be employed in order to construct spin spinor harmonics from scalar harmonics. We provide a very explicit construction of all the scalar and spin harmonics. In a follow-up paper, we shall employ the results we obtain here in order to discuss dimensional reductions and consistent reductions on the Wu manifold.

United States

Cameron Gibson

Okan Günel

Gabriel Larios

C. Pope

Spin $\textit{h}$ structure, scalar and charged spinor eigenfunctions on the SU(3)/SO(3) Wu manifold

We present a first-principles, non-perturbative worldline instanton analysis of vacuum decay in the non-abelian Yang-Mills root of a Schwarzschild background. We recover the gauge theory color-thermal spectrum as a topological winding mode. The double copy maps vacuum response from the gauge theory directly to the gravity theory. Furthermore, the decay exponent acquires a universal quadratic correction from color charge conservation, showing that the double copy correctly captures the non-linear backreaction as required for unitarity.

John Carrasco

Yaxi Chen

Nicolas Pavao

Aslan Seifi

Nonperturbative double copy: worldline instantons, color thermality, and backreaction

We construct the index saddle for the supersymmetric F1-P black ring. Our construction proceeds by taking a supersymmetric limit of a non-supersymmetric doubly spinning F1-P black ring. We express the resulting saddle as a three-center Bena-Warner solution. The black ring saddle possesses a finite-area event horizon, yet the two-derivative index vanishes. The solution is singular on certain subspaces of the horizon, where higher-derivative corrections are expected to become important. We argue that, once such corrections are taken into account, the solution can yield a finite result. In particular, we present a scaling analysis showing that the index agrees with the microscopic result, up to an overall numerical constant that cannot be fixed by the scaling argument alone. This analysis applies only within a restricted region of parameter space, whose full significance is not yet fully understood.

India

Pavan Dharanipragada

China

Gurmeet Punia

Amitabh Virmani

Index saddle for supersymmetric F1-P black ring

We construct the graviton propagator in de Sitter space in a one-parameter family of non-covariant gauges. This family generalizes the simple gauge in which most graviton loop computations in de Sitter space have been performed. The resulting propagator has a relatively simple form and will facilitate checks of the gauge dependence of one-loop computations and proposed observables.

Czechia

Dražen Glavan

Graviton propagator in de Sitter space in a simple one-parameter gauge

The measurement of the Higgs self-coupling is considered the next milestone in the study of the Higgs boson properties. At future $\textit{e}$ $\textit{e}$ facilities below the double Higgs production threshold, this is extracted from the $\textit{Zh}$ production cross-section, which is sensitive to the trilinear coupling at the one-loop level. At the same perturbative order, potential effects beyond the Standard Model (SM) may affect the Higgstrahlung rate and distort the self-coupling determination. We study the question focusing especially on contact interactions containing two electron and two top-quark fields. We conclude that, in the context of FCC-ee and its planned runs at different energies, $\textit{eett}$ interactions change the Higgs self-coupling sensitivity below the percent level. Even in the most pessimistic scenarios, we confirm a robust sensitivity of the order of 17% at the 1$\textit{σ}$ confidence level under the assumption of otherwise SM-like Higgs couplings. A crucial role in these results is played by the measurement of fermion pair production above the $\textit{Z}$ resonance.

Germany

Lukas Allwicher

Christophe Grojean

Lucine Tabatt

Could electron-top interactions spoil the measurement of the Higgs trilinear? A quantitative estimate at future lepton colliders

We compute the contour integral for the partition function of an $$ \mathcal{N} $$ = 2 SU(2) topologically twisted theory on $$ {\mathbbm{CP}}^2 $$ , dimensionally reducing from an $$ \mathcal{N} $$ = 1 theory on $\textit{S}$ . Earlier works presented the partition function as a sum over three equivariant fluxes, one for each toric divisor of $$ {\mathbbm{CP}}^2 $$ . Our result depends only on a single physical flux, assigned to the non-trivial two-cycle of the manifold. The reduced summation over fluxes is compensated by a contour of integration, arising from a different solution of the BPS equations, which captures more poles in each topological sector. As our observable involves a position-dependent Yang-Mills coupling, we compute new equivariant invariants of $$ {\mathbbm{CP}}^2 $$ , which reduce to Donaldson invariants in the non-equivariant limit. Stability conditions of gauge bundles over $$ {\mathbbm{CP}}^2 $$ appear intrinsically via the dimensional reduction.

Italy

Lorenzo Ruggeri

Contour integral for the partition function of $$ \mathcal{N} $$ = 2 topologically twisted on $$ {\mathbbm{CP}}^2 $$ and physical fluxes

We examine whether the Teleparallel Equivalent of General Relativity (TEGR) can be formulated as a gauge theory in the language of connections on principal bundles. We argue in favor of using either the affine bundle with the Poincaré group or, equivalently, the orthonormal frame bundle with the Lorentz group as the structure group. Following the framework of Trautman — where gauge symmetries are determined using the absolute elements — we set to identify the absolute elements and gauge symmetries of TEGR. The triviality of the field equations for metric teleparallel connection raises the question of whether it should be treated as a dynamical variable. If the connection is treated as dynamical, then the only absolute element is the canonical 1-form of the frame bundle, and the gauge group of TEGR is the full diffeomorphism group. If the connection is considered as non-dynamical, we show that its treatment as an absolute element leads to problems of not being able to determine the gauge group and its possible non-uniqueness. On the other hand, if the connection is treated as a non-dynamical variable but not as an absolute element, we again recover the whole diffeomorphism group as the gauge group of TEGR.

Slovakia

Sebastian Brezina

Eugenia Boffo

Martin Krššák

Teleparallel gravity from the principal bundle viewpoint

We examine the physical significance of torsion co-cycles in the cohomology of a projective Calabi-Yau three-fold for the (2,2) superconformal field theory (SCFT) associated to the non-linear sigma model with such a manifold as a target space. There are two independent torsion subgroups in the cohomology. While one is associated to an orbifold construction of the SCFT, the other encodes the possibility of turning on a topologically non-trivial flat gerbe for the NS-NS B-field. Inclusion of these data enriches mirror symmetry by providing a refinement of the familiar structures and points to a generalization of the duality symmetry, where the topology of the flat gerbe enters on the same footing as the topology of the underlying manifold.

Peng Cheng

Ilarion Melnikov

France

Ruben Minasian

The stringy geometry of integral cohomology in mirror symmetry

Deconfined quantum critical point (DQCP) describes direct, non-fine-tuned quantum phase transition between two ordered phases that break distinct and seemingly unrelated symmetries, providing a route to continuous phase transition beyond the conventional Ginzburg-Landau paradigm. In this work we extend the DQCP paradigm to systems with $\textit{internal}$ supersymmetry (SUSY), where the on-site Hilbert space furnishes a representation of a Lie superalgebra, and the Hamiltonian is invariant under the corresponding Lie supergroup. Focusing on the minimal supersymmetric generalization of spin SU(2), namely OSp(1|2), we propose a supersymmetric deconfined quantum critical point (sDQCP) between a phase that breaks internal OSp(1|2) and a phase that instead breaks lattice rotation symmetry. We formulate a non-linear sigma model on the supersphere target space that captures the symmetry intertwinement characteristic of the sDQCP, and we further develop a gauge theory description to address its dynamical properties, including an argument for 3D XY critical behavior. Finally, we show that explicitly breaking OSp(1|2) down to SU(2) continuously connects our sDQCP to the conventional DQCP scenario.

Zhi-Qiang Gao

Hui Yang

Yan-Qi Wang

Deconfined quantum criticality with internal supersymmetry