scholarly journals Operator thermalisation in d > 2: Huygens or resurgence

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Julius Engelsöy ◽  
Jorge Larana-Aragon ◽  
Bo Sundborg ◽  
Nico Wintergerst
Keyword(s):  
Wave Equations ◽  
Free Field ◽  
Perturbation Expansion ◽  
Technical Modifications ◽  
Exponential Relaxation ◽  
Huygens Principle ◽  
Free Fields ◽  
Asymptotic Perturbation ◽  
Perturbative Corrections ◽  
Odd Dimensions

Abstract Correlation functions of most composite operators decay exponentially with time at non-zero temperature, even in free field theories. This insight was recently codified in an OTH (operator thermalisation hypothesis). We reconsider an early example, with large N free fields subjected to a singlet constraint. This study in dimensions d > 2 motivates technical modifications of the original OTH to allow for generalised free fields. Furthermore, Huygens’ principle, valid for wave equations only in even dimensions, leads to differences in thermalisation. It works straightforwardly when Huygens’ principle applies, but thermalisation is more elusive if it does not apply. Instead, in odd dimensions we find a link to resurgence theory by noting that exponential relaxation is analogous to non- perturbative corrections to an asymptotic perturbation expansion. Without applying the power of resurgence technology we still find support for thermalisation in odd dimensions, although these arguments are incomplete.

scholarly journals GENERALIZED W3-STRINGS FROM FREE FIELDS

1995 ◽  
Vol 10 (06) ◽  
pp. 515-524 ◽  
Author(s):  
J. M. FIGUEROA-O'FARRILL ◽  
C. M. HULL ◽  
L. PALACIOS ◽  
E. RAMOS
Keyword(s):  
Bosonic Strings ◽  
Free Field ◽  
Space Time ◽  
General Construction ◽  
Special Cases ◽  
Free Fields ◽  
Rule Out ◽  
General Conditions ◽  
String Theories

The conventional quantization of w3-strings gives theories which are equivalent to special cases of bosonic strings. We explore whether a more general quantization can lead to new generalized W3-string theories by seeking to construct quantum BRST charges directly without requiring the existence of a quantum W3-algebra. We study W3-like strings with a direct space-time interpretation — that is, with matter given by explicit free field realizations. Special emphasis is placed on the attempt to construct a quantum W-string associated with the magic realizations of the classical w3-algebra. We give the general conditions for the existence of W3-like strings, and comment on how the known results fit into our general construction. Our results are negative: we find no new consistent string theories, and in particular rule out the possibility of critical strings based on the magic realizations.

Free Quantum Fields

2020 ◽  
pp. 247-260
Author(s):  
Daniel Canarutto
Keyword(s):  
Free Field ◽  
Gauge Fields ◽  
Quantum Field ◽  
Quantum Fields ◽  
Dirac Fields ◽  
Free Fields ◽  
Explicit Expressions

The notion of free quantum field is thoroughly discussed in the linearised setting associated with the choice of a detector. The discussion requires attention to certain details that are often overlooked in the standard literature. Explicit expressions for generic fields, Dirac fields, gauge fields and ghost fields are laid down, as well the ensuing free-field expressions of important functionals. The relations between super-commutators of free fields and propagators, and the canonical super-commutation rules, follow from the above results.

Causal amplitudes and the Yang-Feldman formalism

1957 ◽  
Vol 53 (4) ◽  
pp. 843-847 ◽  
Author(s):  
J. C. Polkinghorne
Keyword(s):  
Field Theory ◽  
Green’S Functions ◽  
Free Field ◽  
Dispersion Relations ◽  
Matrix Elements ◽  
Field Equations ◽  
Commutation Relations ◽  
The Matrix ◽  
Free Fields ◽  
Set Up

ABSTRACTThe Yang-Feldman formalism vising the Feynman-like Green's functions is set up. The corresponding free fields have non-trivial commutation relations and contain information about the scattering. S-matrix elements are simply the matrix elements of anti-normal products of the field φF′(x). These are evaluated, and they give directly expressions used in the theory of causality and dispersion relations. It is possible to formulate field theory in a form in which the fields obey free field equations and the effects of interaction are contained in their commutation relations.

scholarly journals A NOTE ON KERR/CFT AND FREE FIELDS

2010 ◽  
Vol 25 (20) ◽  
pp. 3965-3973 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Black Hole ◽  
Boundary Conditions ◽  
Isometry Group ◽  
Free Field ◽  
Kerr Black Hole ◽  
Virasoro Algebra ◽  
Free Fields ◽  
Horizon Geometry

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL (2, ℝ) × U (1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.

scholarly journals Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) $$ \mathcal{N} $$ = 4 SYM

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Daniele Dorigoni ◽  
Michael B. Green ◽  
Congkao Wen
Keyword(s):  
Modular Forms ◽  
Free Field ◽  
Perturbation Expansion ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Infinite Sums

Abstract The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/$$ {g}_{YM}^2 $$ g YM 2 , and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order ($$ {g}_{YM}^2 $$ g YM 2 N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qkf(gYM), where q = e2πiτ and f(gYM) = O($$ {g}_{YM}^{-2w} $$ g YM − 2 w ) when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form $$ {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) $$ q ¯ k f ̂ g YM , where $$ \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) $$ f ̂ g YM = O g YM 2 w when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.

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