scholarly journals Supersymmetric graphene on squashed hemisphere

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Rajesh Kumar Gupta ◽  
Augniva Ray ◽  
Karunava Sil
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Momentum Tensor ◽  
Gauge Coupling ◽  
Momentum Tensor ◽  
Abelian Gauge ◽  
3 Dimensional ◽  
Point Correlation ◽  
Point Correlation Function ◽  
R Symmetry

Abstract We compute the partition function of $$ \mathcal{N} $$ N = 2 supersymmetric mixed dimensional QED on a squashed hemisphere using localization. Mixed dimensional QED is an abelian gauge theory coupled to charged matter fields at the boundary. The partition function is a function of the complex gauge coupling τ, the choice of R-symmetry and the squashing deformation. The superconformal R-symmetry is determined using the 3-dimensional F-maximization. The free energy as a function of squashing deformation allows computing correlation functions that contain the insertion of the energy-momentum tensor. We compute the 2-point correlation function of the energy-momentum tensor of 3-dimensional theory by differentiating the free energy with respect to the squashing parameter. We comment on the behaviour of the 2-point function as we change the complex coupling τ.

scholarly journals The four-point correlation function of the energy-momentum tensor in the free conformal field theory of a scalar field

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Mirko Serino
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
General Covariance ◽  
Explicit Result ◽  
Conformally Invariant ◽  
Point Correlation ◽  
Point Correlation Function

Abstract We present an explicit momentum space computation of the four-point function of the energy-momentum tensor in 4 spacetime dimensions for the free and conformally invariant theory of a scalar field. The result is obtained by explicit evaluation of the Feynman diagrams by tensor reduction. We work by embedding the scalar field theory in a gravitational background consistently with conformal invariance in order to derive all the terms the correlator consists of and all the Ward identities implied by the requirements of general covariance and anomalous Weyl symmetry. We test all these identities numerically in several kinematic configurations. Mathematica notebooks detailing the step-by-step computation are made publicly available through a GitHub repository (https://github.com/mirkos86/4-EMT-correlation-function-in-a-4d-CFT.). To the best of our knowledge, this is the first explicit result for the four-point correlation function of the energy-momentum tensor in a conformal and non supersymmetric field theory which is readily numerically evaluable in any kinematic configuration.

N=2 SUPERCONFORMAL INTERACTING BOSONIC MODELS

1992 ◽  
Vol 07 (04) ◽  
pp. 345-356 ◽  
Author(s):  
RON COHEN
Keyword(s):  
Free Energy ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Oriented Graph ◽  
Momentum Tensor ◽  
Superconformal Algebra ◽  
Chiral Algebra ◽  
Bosonic Model ◽  
Coset Models

Bosonic representations of N=2 superconformal algebra are studied. We show that the free energy momentum tensor decomposes into an orthogonal sum of the interacting bosonic model (IBM) and a coset-like tensors. We define the notion of flags of models and show that the central charge does not decrease along the flags. We examine the conditions for an arbitrary un-oriented graph to form an IBM. We discuss several properties of the chiral algebra of these models and examine the role of the continuous parameters by studying an example. Finally we discuss the relations between these models and the N=2 superconformal coset models.

scholarly journals Crystal plasticity: The Hamilton-Eshelby stress in terms of the metric in the intermediate configuration

2012 ◽  
Vol 39 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Paolo Mariano
Keyword(s):  
Free Energy ◽  
Energy Momentum Tensor ◽  
Large Strain ◽  
Momentum Tensor ◽  
Classical Field ◽  
Field Theories ◽  
Relative Power ◽  
Eshelby Stress ◽  
Classical Field Theories ◽  
Intermediate Configuration

The Hamilton-Eshelby stress is a basic ingredient in the description of the evolution of point, lines and bulk defects in solids. The link between the Hamilton-Eshelby stress and the derivative of the free energy with respect to the material metric in the plasticized intermediate configuration, in large strain regime, is shown here. The result is a modified version of Rosenfeld-Belinfante theorem in classical field theories. The origin of the appearance of the Hamilton-Eshelby stress (the non-inertial part of the energy-momentum tensor) in dissipative setting is also discussed by means of the concept of relative power.

scholarly journals One-loop corrections to the primordial tensor spectrum from massless isocurvature fields

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hai Siong Tan
Keyword(s):  
Beta Function ◽  
Dimensional Regularization ◽  
Massless Scalar ◽  
Cosmological Perturbation ◽  
Abelian Gauge ◽  
Cosmological Perturbation Theory ◽  
Negative Constant ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Matter Fields

Abstract We study one-loop corrections to the two-point correlation function of tensor perturbations in primordial cosmology induced by massless spectator matter fields. Using the Schwinger-Keldysh formalism in cosmological perturbation theory, we employ dimensional regularization and cutoff regularization to study the finite quantum corrections at one-loop arising from isocurvature fields of the massless scalar, fermion and abelian gauge field which are freely propagating on the FRW spacetime. For all cases, we find a logarithmic running of the form $$ \frac{C}{q^3}\frac{H^4}{M_p^4} $$ C q 3 H 4 M p 4 log $$ \left(\frac{H}{\mu}\right) $$ H μ where C is a negative constant related to the beta function, H is the Hubble parameter at horizon exit and μ is the renormalization scale.

scholarly journals ENERGY AND ENTROPY OF RELATIVISTIC DIFFUSING PARTICLES

2010 ◽  
Vol 25 (31) ◽  
pp. 2683-2695 ◽  
Author(s):  
Z. HABA
Keyword(s):  
Free Energy ◽  
Time Dependence ◽  
Energy Momentum Tensor ◽  
Second Law Of Thermodynamics ◽  
Momentum Tensor ◽  
Second Law ◽  
Entropy Flow ◽  
Fixed Temperature ◽  
Exact Time ◽  
Energy Entropy

We discuss energy–momentum tensor and the second law of thermodynamics for a system of relativistic diffusing particles. We calculate the energy and entropy flow in this system. We obtain an exact time-dependence of energy, entropy and free energy of a beam of photons in a reservoir of a fixed temperature.

scholarly journals DARK MATTER WITH VARIABLE MASSES

1993 ◽  
Vol 02 (01) ◽  
pp. 85-95 ◽  
Author(s):  
JUAN GARCÍA-BELLIDO
Keyword(s):  
Dark Matter ◽  
Galaxy Formation ◽  
Cold Dark Matter ◽  
Spiral Galaxies ◽  
Energy Momentum Tensor ◽  
Gauge Coupling ◽  
Momentum Tensor ◽  
Primordial Nucleosynthesis ◽  
Effective Theories ◽  
Dilaton Coupling

String effective theories contain a dilaton scalar field which couples to gravity, matter and radiation. In general, particle masses will have different dilaton couplings. We can always choose a conformal frame in which baryons have constant masses while (nonbaryonic) dark matter have variable masses, in the context of a scalar-tensor gravity theory. We are interested in the phenomenology of this scenario. Dark matter with variable masses could have a measurable effect on the dynamical motion of the halo of spiral galaxies, which may affect cold dark matter models of galaxy formation. As a consequence of variable masses, the energy-momentum tensor is not conserved; there is a dissipative effect, due to the dilaton coupling, associated with a “dark entropy” production. In particular, if axions had variable masses they could be diluted away, thus opening the “axion window.” Assuming that dark matter with variable masses dominates the cosmological evolution during the matter era, it will affect the primordial nucleosynthesis predictions on the abundances of light elements. Furthermore, the dilaton also couples to radiation in the form of a variable gauge coupling. Experimental bounds will constrain the parameters of this model.

THE GAUSSIAN APPROXIMATION FOR THE λφ4THEORY AT FINITE TEMPERATURE REVISITED

1991 ◽  
Vol 06 (26) ◽  
pp. 4579-4638 ◽  
Author(s):  
FRÉDÉRIQUE GRASSI ◽  
RÉMI HAKIM ◽  
HORACIO D. SIVAK
Keyword(s):  
Free Energy ◽  
Effective Mass ◽  
Effective Potential ◽  
Finite Temperature ◽  
Energy Momentum Tensor ◽  
Gaussian Approximation ◽  
Dimensional Regularization ◽  
Momentum Tensor ◽  
Effects Of Temperature ◽  
Physical Quantities

This paper is devoted to a systematic study of the λφ4 theory in the Gaussian approximation and at finite temperature. Although our results can be extended in a straightforward manner to other dimensions, only the case of four (1+3) dimensions is dealt with here. The Gaussian approximation is implemented via the moments of the field φ, a method somewhat simpler than the Gaussian functional approach. Furthermore, the effective potential (equivalently, the free energy) is calculated through the evaluation of the energy-momentum tensor of quasiparticles endowed with an effective mass. This effective mass generally obeys a gap equation, which is analyzed and solved. Besides the “precarious” solution of Stevenson or the “autonomous” one of Stevenson and Tarrach, which are recovered and rediscussed, several nonperturbative solutions, either exhibiting “spontaneous symmetry breaking” or not, are obtained with the help of systematic expansions of various physical quantities in powers of ε, the parameter occurring in the dimensional regularization scheme used throughout this paper. The effects of temperature are discussed in detail: phase transitions in the precarious or autonomous solutions occur. Other simple Gaussian (but not minimal) solutions for the effective potential (free energy) are also obtained.

Three-dimensional study on the interconnection and shape of crystals in a graphic granite by X-ray CT and image analysis

2000 ◽  
Vol 64 (5) ◽  
pp. 945-959 ◽  
Author(s):  
S. Ikeda ◽  
T. Nakano ◽  
Y. Nakashima
Keyword(s):  
Image Analysis ◽  
Correlation Function ◽  
Three Dimensions ◽  
Ct Scanner ◽  
X Ray ◽  
Binary Images ◽  
3 Dimensional ◽  
Ct Value ◽  
Point Correlation ◽  
Point Correlation Function

AbstractThe technique of investigating 3-dimensional interconnections and the shapes of crystals in a rock by X-ray computerized tomography (CT) and image analysis was developed using a graphic granite specimen as an example. Fifty 2-dimensional tomographic images (slices) of the graphic granite were obtained ‘non-destructively’ using a medical X-ray CT scanner. Since a CT value of the specimen was decreased with increasing cross-sectional sample area by the effect of beam-hardening, the CT value was corrected using the area of each slice. Binary images of the slices were made comparing one of them with a thin-section of the slice. Using the binary images, connection analysis of quartz rods in the graphic granite specimen was performed on the basis of percolation theory (cluster labelling). This analysis showed that at least 89.9% of the quartz rods were connected in three dimensions. Furthermore, the 3-dimensional shape of the quartz rods was analysed using the 2-point correlation function calculated from the binary images. The average shape of the quartz rods was obtained by fitting an ellipsoid to the high-value region of the 2-point correlation function. The elongation axis of the ellipsoid agreed well with the crystallographicc-axes of the quartz rods.

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