scholarly journals Thermal correlation functions in CFT and factorization

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J. G. Russo
Keyword(s):  
Free Energy ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Analytic Formula ◽  
Black Brane ◽  
Factorization Property ◽  
Point Function ◽  
Universal Formula ◽  
Thermal Correlation ◽  
Semiclassical Regime

Abstract We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in d dimensions in terms of the c-anomaly coefficient. By including α′ corrections to the black brane background, we reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula. When the dimensions satisfy ∆i = ∆j + ∆k, the thermal 3-point function satisfies a factorization property. We argue that in d > 2 factorization is a reflection of the semiclassical regime.

scholarly journals Correlation functions in finite temperature CFT and black hole singularities

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J.G. Russo
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Proper Time ◽  
Black Brane ◽  
Point Function ◽  
Black Hole Singularity ◽  
Point Correlation ◽  
Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

scholarly journals The planar limit of $$ \mathcal{N} $$ = 2 chiral correlators

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Bartomeu Fiol ◽  
Alan Rios Fukelman
Keyword(s):  
Free Energy ◽  
Infinite Number ◽  
Correlation Functions ◽  
Hermitian Matrix ◽  
Hooft Coupling ◽  
Planar Limit ◽  
Single Trace ◽  
Hermitian Matrix Model ◽  
Combinatorial Expression ◽  
Do So

Abstract We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of $$ \mathcal{N} $$ N = 2 SQCD on S4, to all orders in the ’t Hooft coupling. In order to do so, we first obtain a combinatorial expression for the planar free energy of a hermitian matrix model with an infinite number of arbitrary single and double trace terms in the potential; this solution might have applications in many other contexts. We then use these results to evaluate the analogous planar correlation functions on ℝ4. Specifically, we compute all the terms with a single value of the ζ function for a few planar 2- and 3-point functions, and conjecture general formulas for these terms for all 2- and 3-point functions on ℝ4.

Review of the holographic Lifshitz theory

2014 ◽  
Vol 29 (24) ◽  
pp. 1430049 ◽  
Author(s):  
Chanyong Park
Keyword(s):  
Field Theory ◽  
Finite Temperature ◽  
Quasinormal Mode ◽  
Thermodynamic Quantities ◽  
Black Brane ◽  
Zero Temperature ◽  
Hydrodynamic Properties ◽  
Relativistic Field ◽  
Thermal Entropy ◽  
Lifshitz Theory

We review interesting results achieved in recent studies on the holographic Lifshitz field theory. The holographic Lifshitz field theory at finite temperature is described by a Lifshitz black brane geometry. The holographic renormalization together with the regularity of the background metric allows to reproduce thermodynamic quantities of the dual Lifshitz field theory where the Bekenstein–Hawking entropy appears as the renormalized thermal entropy. All results satisfy the desired black brane thermodynamics. In addition, hydrodynamic properties are further reviewed in which the holographic retarded Green functions of the current and momentum operators are studied. In a nonrelativistic Lifshitz field theory, intriguingly, there exists a massive quasinormal mode at finite temperature whose effective mass is linearly proportional to temperature. Even at zero temperature and in the nonzero momentum limit, a quasinormal mode still remains unlike the dual relativistic field theory. Finally, we account for how adding impurity modifies the electric property of the nonrelativistic Lifshitz theory.

scholarly journals Thermal correlation functions of twisted quantum fields

2010 ◽  
Vol 82 (2) ◽  
Author(s):  
Prasad Basu ◽  
Rahul Srivastava ◽  
Sachindeo Vaidya
Keyword(s):  
Correlation Functions ◽  
Quantum Fields ◽  
Thermal Correlation

scholarly journals Color singlet and adjoint free energy at finite temperature

2009 ◽  
Author(s):  
Alexei Bazavov ◽  
Peter Petreczky ◽  
Alexander Velytsky
Keyword(s):  
Free Energy ◽  
Finite Temperature ◽  
Color Singlet

scholarly journals CASIMIR ENERGY OF A DILUTE DIELECTRIC BALL AT ZERO AND FINITE TEMPERATURE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 790-793 ◽  
Author(s):  
V. V. NESTERENKO ◽  
G. LAMBIASE ◽  
G. SCARPETTA
Keyword(s):  
Free Energy ◽  
Electromagnetic Field ◽  
Angular Momentum ◽  
High Temperature ◽  
Finite Temperature ◽  
Bessel Functions ◽  
Thermodynamic Characteristics ◽  
Casimir Energy ◽  
Addition Theorem ◽  
Temperature Expansion

The basic results in calculations of the thermodynamic functions of electromagnetic field in the background of a dilute dielectric ball at zero and finite temperature are presented. Summation over the angular momentum values is accomplished in a closed form by making use of the addition theorem for the relevant Bessel functions. The behavior of the thermodynamic characteristics in the low and high temperature limits is investigated. The T3-term in the low temperature expansion of the free energy is recovered (this term has been lost in our previous calculations).

QUANTUM MAGNETIC VORTICES AT FINITE TEMPERATURE IN (3 + 1)-D

2000 ◽  
Vol 15 (11n12) ◽  
pp. 731-735
Author(s):  
E. C. MARINO ◽  
D. G. G. SASAKI
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Large Distance ◽  
Finite Temperature ◽  
Higgs Model ◽  
Magnetic Vortex ◽  
Zero Temperature ◽  
Magnetic Vortices ◽  
Vortex Lines ◽  
Distance Behavior

We study the effect of a finite temperature on the correlation function of quantum magnetic vortex lines in the framework of the (3 + 1)-dimensional Abelian Higgs model. The vortex energy is inferred from the large distance behavior of these correlation functions. For large straight vortices of length L, we obtain that the energy is proportional to TL2 differently from the zero temperature result which is proportional to L. The case of closed strings is also analyzed. For T = 0, we evaluate the correlation function and energy of a large ring. Finite closed vortices do not exist as genuine excitations for any temperature.

scholarly journals FREE ENERGY DECREASES ALONG WILSON RENORMALIZATION GROUP TRAJECTORIES

1995 ◽  
Vol 10 (21) ◽  
pp. 1543-1548 ◽  
Author(s):  
VIPUL PERIWAL
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Spectral Representation ◽  
Point Function ◽  
Cutoff Function ◽  
Wilson Renormalization Group

The free energy is shown to decrease along Wilson renormalization group trajectories, in a dimension-independent fashion, for d>2. The argument assumes the monotonicity of the cutoff function, and positivity of a spectral representation of the two-point function. The argument is valid for all orders in perturbation theory.

Free-Energy Calculations

2006 ◽  
Author(s):  
Vasily Bulatov ◽  
Wei Cai
Keyword(s):  
Free Energy ◽  
Melting Temperature ◽  
Open System ◽  
Finite Temperature ◽  
Liquid State ◽  
Crystalline State ◽  
Minimum Energy ◽  
Temperature Limit ◽  
Free Energy Calculations ◽  
Energy Calculations

Free energy is of central importance for understanding the properties of physical systems at finite temperatures. While in the zero temperature limit the system should evolve to a state of minimum energy (Section 2.3), this is not necessarily the case at a finite temperature. When an open system exchanges energy with the outside world (a thermostat) and maintains a constant temperature, its evolution proceeds towards minimizing its free energy. For example, a crystal turns into a liquid when the temperature exceeds its melting temperature precisely because the free energy of the liquid state becomes lower than that of the crystalline state. In the context of dislocation simulations, free energy is all important when one has to decide which of the possible core configurations the dislocation is likely to adopt at a given temperature.

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