In this paper, the existence of a massive dark photon, associated with a new gauge group is considered. The dark photon can be kinetically mixed with the photon. To study some applications, the thermo field dynamics formalism is used. Exploring the topological structure of this approach, the influence of dark photons on the Stefan–Boltzmann law and the Casimir effect at zero and finite temperature is calculated.

Brazil

V. Prata

A. Santos

Canada

Faqir Khanna

Stefan–Boltzmann law and Casimir effect for dark photons

We revisit the relation between the anomalies in four and six dimensions and the Chern-Simons couplings one dimension below. While the dimensional reduction of chiral theories is well-understood, the question which three and five-dimensional theories can come from a general circle reduction, and are hence liftable, is more subtle. We argue that existence of an anomaly cancellation mechanism is a necessary condition for liftability. In addition, the anomaly cancellation and the CS couplings in six and five dimensions respectively determine the central charges of string-like BPS objects that cannot be consistently decoupled from gravity, a.k.a. supergravity strings. Following the completeness conjecture and requiring that their worldsheet theory is unitary imposes bounds on the admissible theories. We argue that for the anomaly-free six-dimensional theories it is more advantageous to study the unitarity constraints obtained after reduction to five dimensions. In general these are slightly more stringent and can be cast in a more geometric form, highly reminiscent of the Kodaira positivity condition (KPC). Indeed, for the F-theoretic models which have an underlying Calabi-Yau threefold these can be directly compared. The unitarity constraints (UC) are in general weaker than KPC, and maybe useful in understanding the consistent models without F-theoretic realisation. We catalogue the cases when UC is more restrictive than KPC, hinting at more refined hidden structure in elliptic Calabi-Yau threefolds with certain singularity structure.

France

Peng Cheng

Ruben Minasian

Germany

Stefan Theisen

Anomalies as obstructions: from dimensional lifts to swampland

We construct a class of interacting (<math><mrow><mi>d</mi><mo>−</mo><mn>2</mn></mrow></math>)-form theories in <math><mi>d</mi></math> dimensions that are “third-way” consistent. This refers to the fact that the interaction terms in the <math><mi>p</mi></math>-form field equations of motion neither come from the variation of an action nor are they off-shell conserved on their own. Nevertheless, the full equation is still on-shell consistent. Various generalizations, e.g., coupling them to (<math><mrow><mi>d</mi><mo>−</mo><mn>3</mn></mrow></math>)-forms, where three algebras play a prominent role, are also discussed. The method to construct these models also easily recovers the modified three-dimensional Yang-Mills theory obtained earlier and straightforwardly allows for higher derivative extensions.

Matteo Broccoli

Türkiye

Nihat Sadik Deger

Third Way to Interacting <math><mrow><mi>p</mi></mrow></math>-Form Theories

The S-matrix for each chiral sector of Liouville theory on a cylinder is computed from the loop expansion of correlation functions of a one-dimensional field theory on a circle with a non-local kinetic energy and an exponential potential. This action is the Legendre transform of the generating function of semiclassical scattering amplitudes. It is derived from the relation between asymptotic in- and out-fields. Its relevance for the quantum scattering process is demonstrated by comparing explicit loop diagrams computed from this action with other methods of computing the S-matrix, which are also developed.

Georgia

George Jorjadze

On the S-matrix of Liouville theory

The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established, and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.

S.C. Ulhoa

R.G.G. Amorim

J.S. da Cruz Filho

A.F. Santos

F.C. Khanna

Spin-1/2 Particles in Phase Space: Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

Gravitons are described by the propagator in teleparallel gravity in nearly flat space-time. Finite temperature is introduced by using Thermofield Dynamics formalism. The gravitational Casimir effect and Stefan-Boltzmann law are calculated as a function of temperature. Then an equation of state for gravitons is determined.

T.F. Furtado

On Gravitational Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

We use the scalar field constructed in phase space to analyze the analogous Stefan-Boltzmann law and Casimir effect, both of them at finite temperature. The temperature is introduced by Thermo Field Dynamics (TFD) formalism and the quantities are analyzed once projected in the space of coordinates. We show that using the framework of phase space it is possible to introduce a thermal energy which is related to temperature as it vanishes when the temperature tends to zero. In fact given such a correlation the formalism of TFD is equivalent when project is in momenta space when compared to coordinates space.

Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature

Local terms in the Operator Product Expansion in Superconformal Theories with extended supersymmetry are identified. Assuming a factorized structure for these terms their contributions are discussed.

Israel

Adam Schwimmer

Moduli anomalies and local terms in the operator product expansion

Non-conformal supercurrents in six dimensions are described, which contain the trace of the energy-momentum tensor and the gamma-trace of the supersymmetry current amongst their component fields. Within the superconformal approach to N = 1 , 0 $$ \mathcal{N}=\left(1,\ 0\right) $$ supergravity, we present various distinct non-conformal supercurrents, one of which is associated with an O 2 $$ \mathcal{O}(2) $$ (or linear) multiplet compensator, while another with a tensor multiplet compensator. We also derive an infinite class of non-conformal supercurrents involving O n $$ \mathcal{O}(n) $$ multiplets with n &gt; 2. As an illustrative example we construct the relaxed hypermultiplet in supergravity. Finally, we put forward a non-conformal supercurrent in the N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ supersymmetric case.

Australia

Sergei Kuzenko

Joseph Novak

Non-conformal supercurrents in six dimensions

Within the framework of six-dimensional N=(1,0) conformal supergravity, we introduce new off-shell multiplets O⁎(n) , where n=3,4,… , and use them to construct higher-rank extensions of the linear multiplet action. The O⁎(n) multiplets may be viewed as being dual to well-known superconformal O(n) multiplets. We provide prepotential formulations for the O(n) and O⁎(n) multiplets coupled to conformal supergravity. For every O⁎(n) multiplet, we construct a higher derivative invariant which is superconformal on arbitrary superconformally flat backgrounds. We also show how our results can be used to construct new higher derivative actions in supergravity.