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Peter Schupp

Publications and source records attributed to Peter Schupp.

At least 19 recordsLinked to original sources
arXiv2024

Graded Geometry and Tensor Gauge Theories

We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that a given Lagrangian describes the dynamics of any type of bosonic tensor field even though the corresponding explicit expressions in terms of local field components and their derivatives look rather different. Aside from free fields and their kinetic terms, we also consider higher derivative interaction terms that lead to second order field equations. For scalars, differential forms and bipartite tensors, these are identified with Galileon theories, written in a simple yet elegant form as a generalised kinetic term, and are gauge invariant by construction. For fields of spin higher than 2, we illustrate the candidate Galileon-like interactions and argue that full gauge invariance and locality cannot be simultaneously maintained.

hep-th↗
arXiv2024

An algebraic formulation of nonassociative quantum mechanics

We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is based on using the universal enveloping algebra of a general nonassociative algebra to introduce a generalized notion of associative composition product. We formulate properties of states together with notions of trace, and use them to develop GNS constructions. We describe Heisenberg and Schrödinger pictures of completely positive dynamics, and we illustrate our formalism on the explicit examples of finite-dimensional matrix Jordan algebras as well as the octonion algebra.

quant-ph↗
arXiv2022

Axion gravitodynamics, Lense-Thirring effect, and gravitational waves

We investigate physical implications of a gravitational analog of axion electrodynamics with a parity-violating gravitoelectromagnetic theta term. This is related to the Nieh-Yan topological invariant in gravity with torsion, in contrast to the well-studied gravitational Chern-Simons term quadratic in curvature, coupled via a dynamical axionlike scalar field. Axion gravitodynamics is the corresponding linearized theory. We find that potentially observable effects are over 80 orders of magnitude stronger than for its Chern-Simons counterpart and could be in reach for detection by experiments in the near future. For a near-Earth scenario, we derive corrections to the Lense-Thirring effect and compare them to data from satellite-based experiments (Gravity Probe B). For gravitational waves, we find modified dispersion relations, derive the corresponding polarization-dependent modified group and phase velocities, and compare them to data from neutron star mergers (GW170817) to derive even stronger bounds.

gr-qc↗
arXiv2022

Wehrl entropy, coherent states and quantum channels

We review Wehrl's definition of a semiclassical entropy in terms of coherent states and give an introductory overview of Lieb's conjecture, its proof (including earlier results), generalizations, and the role of covariant quantum channels in this context. These structures motivate an alternative definition of coherent states and have interesting physical applications and implications.

quant-ph↗
arXiv2020

A unified approach to standard and exotic dualizations through graded geometry

Gauge theories can often be formulated in different but physically equivalent ways, a concept referred to as duality. Using a formalism based on graded geometry, we provide a unified treatment of all parent theories for different types of standard and exotic dualizations. Our approach is based on treating tensor fields as functions of a certain degree on graded supermanifolds equipped with a suitable number of odd coordinates. We present a universal two-parameter first order action for standard and exotic electric/magnetic dualizations and prove in full generality that it yields two dual second order theories with the desired field content and dynamics. Upon choice of parameters, the parent theory reproduces (i) the standard and exotic duals for p-forms and (ii) the standard and double duals for (p,1) bipartite tensor fields, such as the linearized graviton and the Curtright field. Moreover, we discuss how deformations related to codimension-1 branes are included in the parent theory.

hep-th↗
arXiv2020

Torsion-induced gravitational $θ$ term and gravitoelectromagnetism

Motivated by the analogy between a weak field expansion of general relativity and Maxwell's laws of electrodynamics, we explore physical consequences of a parity violating $θ$ term in gravitoelectromagnetism. This is distinct from the common gravitational $θ$ term formed as a square of the Riemann tensor. Instead it appears as a product of the gravitoelectric and gravitomagnetic fields in the Lagrangian, similar to the Maxwellian $θ$ term. We show that this sector can arise from a quadratic torsion term in nonlinear gravity. In analogy to the physics of topological insulators, the torsion-induced $θ$ parameter can lead to excess mass density at the interface of regions where $θ$ varies and consequently it generates a correction to Newton's law of gravity. We discuss also an analogue of the Witten effect for gravitational dyons.

gr-qc↗
arXiv2020

Dual gravity with $R$ flux from graded Poisson algebra

We suggest a new action for a ``dual'' gravity in a stringy $R$, $Q$ flux background. The construction is based on degree-$2$ graded symplectic geometry with a homological vector field. The structure we consider is non-canonical and features a curvature-free connection. It is known that the data of Poisson structures of degree $2$ with a Hamiltonian correspond to a Courant algebroid on $TM \oplus T^{*}M$, the bundle of generalized geometry. With the bracket for the Courant algebroid and a further bracket which resembles the Lie bracket of vector fields, we get a connection with non-zero curvature for the bundle of generalized geometry. The action is the (almost) Hilbert-Einstein action for that connection.

hep-th↗
arXiv2019

Deformed graded Poisson structures, Generalized Geometry and Supergravity

In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view of graded geometry, introducing an approach based on deformations of graded Poisson structures and derive the corresponding gravity actions. We consider in particular natural deformations of the $2$-graded symplectic manifold $T^{*}[2]T[1]M$ that are based on a metric $g$, a closed Neveu-Schwarz $3$-form $H$ (locally expressed in terms of a Kalb-Ramond 2-form $B$) and a scalar dilaton $ϕ$. The derived bracket formalism relates this structure to the generalized differential geometry of a Courant algebroid, which has the appropriate stringy symmetries, and yields a connection with non-trivial curvature and torsion on the generalized "doubled" tangent bundle $E \cong TM \oplus T^{*}M$. Projecting onto $TM$ with the help of a natural non-isotropic splitting of $E$, we obtain a connection and curvature invariants that reproduce the NS-NS sector of supergravity in 10~dimensions. Further results include a fully generalized Dorfman bracket, a generalized Lie bracket and new formulas for torsion and curvature tensors associated to generalized tangent bundles. A byproduct is a unique Koszul-type formula for the torsionful connection naturally associated to a non-symmetric metric, which resolves ambiguity problems and inconsistencies of traditional approaches to non-symmetric gravity theories.

hep-th↗
arXiv2019

Linking multipole vectors and pseudoentropies for CMB analysis

Multipole vectors and pseudoentropies provide powerful tools for a numerically fast and vivid investigation of possible statistically anisotropic, respectively non-Gaussian signs in CMB temperature fluctuations. After reviewing and linking these two conceptions we compare their application to data analysis using the Planck 2015 NILC full sky map.

astro-ph.CO↗
arXiv2019

Entropy methods for CMB analysis of anisotropy and non-Gaussianity

We propose several pseudoentropy measures that agree well with the Wehrl entropy, but are significantly faster to compute. All of them are rotationally invariant measures of entanglement very sensitive to non-Gaussianity, anisotropy, and statistical dependence of spherical harmonic coefficients. We provide a simple proof that the projection pseudoentropy converges to the Wehrl entropy with increasing dimensionality of the ancilla projection space. Furthermore, for $l=2$, we show that both the Wehrl entropy and the angular pseudoentropy can be expressed as functions of the squared chordal distance of multipole vectors. We also show that the angular pseudoentropy can distinguish between Gaussian and non-Gaussian temperature fluctuations at large multipoles and henceforth provides a non-brute-force method for identifying non-Gaussianities. This allows us to study possible hints of statistical anisotropy and non-Gaussianity in the CMB up to multipole $l=1000$ using Planck 2015/2018, and WMAP 7-yr data. We find that $l=5$ and $28$ have a large entropy at $2$--$3σ$ significance and a slight hint towards a connection of this with the cosmic dipole. On a wider range of large angular scales we do not find indications of isotropy/Gaussianity violation. We also find a small-scale range, $l\in[895,905]$, that is incompatible with the assumptions at about $3σ$ level, although how much this significance can be reduced by taking into account the selection effect is left as an open question. We find overall similar results in our analysis of the 2015 and the 2018 data. Finally, we also demonstrate how a range of angular momenta can be studied with the range angular pseudoentropy. Our main purpose is to introduce the methods, analyze their mathematical background, and demonstrate their usage for providing researchers in this field with an additional tool.

astro-ph.CO↗
arXiv2017

Tensor Galileons and Gravity

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian $p$-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to $p$-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

hep-th↗
arXiv2015

Generalized geometry and non-symmetric gravity

Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to the study of the low-energy effective closed string gravity actions.

hep-th↗
arXiv2014

Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics

We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux.

hep-th↗
arXiv2014

Extended generalized geometry and a DBI-type effective action for branes ending on branes

Starting from the usual bosonic membrane action, we develop the geometry suitable for the description of $p$-brane backgrounds. Using the tools of generalized geometry we derive the generalization of string open-closed relations. Nambu-Poisson structures are used to generalize the concept of semiclassical noncommutativity of $D$-branes governed by Poisson tensor. We naturally describe the correspondence of recently proposed commutative and noncommutative versions of an effective action for $p$-branes ending on a $p'$-brane. We calculate the power series expansion of the action in background independent gauge. Leading terms in the double scaling limit are given by a generalization of a (semi-classical) matrix model.

hep-th↗
arXiv2014

Nambu-Poisson Gauge Theory

We generalize noncommutative gauge theory using Nambu-Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg-Witten map. We construct a covariant Nambu-Poisson gauge theory action, give its first order expansion in the Nambu-Poisson tensor and relate it to a Nambu-Poisson matrix model.

hep-th↗
arXiv2014

Nonassociative geometry and twist deformations in non-geometric string theory

We describe nonassociative deformations of geometry probed by closed strings in non-geometric flux compactifications of string theory. We show that these non-geometric backgrounds can be geometrised through the dynamics of open membranes whose boundaries propagate in the phase space of the target space compactification, equiped with a twisted Poisson structure. The effective membrane target space is determined by the standard Courant algebroid over the target space twisted by an abelian gerbe in momentum space. Quantization of the membrane sigma-model leads to a proper quantization of the non-geometric background, which we relate to Kontsevich's formalism of global deformation quantization that constructs a noncommutative nonassociative star product on phase space. We construct Seiberg-Witten type maps between associative and nonassociative backgrounds, and show how they may realise a nonassociative deformation of gravity. We also explain how this approach is related to the quantization of certain Lie 2-algebras canonically associated to the twisted Courant algebroid, and cochain twist quantization using suitable quasi-Hopf algebras of symmetries in the phase space description of R-space which constructs a Drinfel'd twist with non-trivial 3-cocycle. We illustrate and apply our formalism to present a consistent phase space formulation of nonassociative quantum mechanics.

hep-th↗
arXiv2013

p-Brane Actions and Higher Roytenberg Brackets

Motivated by the quest to understand the analog of non-geometric flux compactification in the context of M-theory, we study higher dimensional analogs of generalized Poisson sigma models and corresponding dual string and p-brane models. We find that higher generalizations of the algebraic structures due to Dorfman, Roytenberg and Courant play an important role and establish their relation to Nambu-Poisson structures.

hep-th↗