The spectral representation of the two-point function and local commutativity

1962 ◽  
Vol 24 (6) ◽  
pp. 1147-1159 ◽  
Author(s):  
L. Lovitch ◽  
Y. Tomozawa
Keyword(s):  
Spectral Representation ◽  
Point Function ◽  
Local Commutativity

scholarly journals Loops in AdS: from the spectral representation to position space. Part II

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dean Carmi
Keyword(s):  
Spectral Representation ◽  
Tree Level ◽  
Point Function ◽  
Position Space ◽  
Gross Neveu Model ◽  
Loop Amplitudes

Abstract We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-N conformal Gross Neveu model on AdS3. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

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.

scholarly journals PCT theorem, Wightman axioms and conformal bootstrap

2021 ◽  
Vol 36 (11) ◽  
pp. 2150072
Author(s):  
Jnanadeva Maharana
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Analytic Continuation ◽  
Crucial Role ◽  
Point Function ◽  
Bootstrap Equation ◽  
Conformal Field ◽  
Local Commutativity ◽  
Conformal Bootstrap ◽  
Wightman Axioms

The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four-point function. The equivalence between PCT theorem and weak local commutativity, due to Jost plays a very crucial role in axiomatic field theory. The theorem is suitably adopted for conformal field theory to derive the desired equations in CFT. We demonstrate that the two Wightman functions are analytic continuation of each other.

scholarly journals General structure of fermion two-point function and its spectral representation in a hot magnetized medium

2018 ◽  
Vol 97 (3) ◽  
Author(s):  
Aritra Das ◽  
Aritra Bandyopadhyay ◽  
Pradip K. Roy ◽  
Munshi G. Mustafa
Keyword(s):  
Spectral Representation ◽  
General Structure ◽  
Point Function

Holographic renormalization, one-point functions, and a two-point function

2014 ◽  
pp. 406-409
Author(s):  
Jorge Casalderrey-Solana ◽  
Hong Liu ◽  
David Mateos ◽  
Krishna Rajagopal ◽  
Urs Achim Wiedemann
Keyword(s):  
Point Function ◽  
Holographic Renormalization

scholarly journals The 3d $$ \mathcal{N} $$ = 6 bootstrap: from higher spins to strings to membranes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Damon J. Binder ◽  
Shai M. Chester ◽  
Max Jerdee ◽  
Silviu S. Pufu
Keyword(s):  
Block Decomposition ◽  
Point Function ◽  
Present Evidence ◽  
Bootstrap Techniques ◽  
Wide Range ◽  
Higher Spin ◽  
Tensor Multiplet ◽  
Higher Spins ◽  
M Theory ◽  
Chern Simons

Abstract We study the space of 3d $$ \mathcal{N} $$ N = 6 SCFTs by combining numerical bootstrap techniques with exact results derived using supersymmetric localization. First we derive the superconformal block decomposition of the four-point function of the stress tensor multiplet superconformal primary. We then use supersymmetric localization results for the $$ \mathcal{N} $$ N = 6 U(N)k × U(N + M)−k Chern-Simons-matter theories to determine two protected OPE coefficients for many values of N, M, k. These two exact inputs are combined with the numerical bootstrap to compute precise rigorous islands for a wide range of N, k at M = 0, so that we can non-perturbatively interpolate between SCFTs with M-theory duals at small k and string theory duals at large k. We also present evidence that the localization results for the U(1)2M × U (1 + M)−2M theory, which has a vector-like large-M limit dual to higher spin theory, saturates the bootstrap bounds for certain protected CFT data. The extremal functional allows us to then conjecturally reconstruct low-lying CFT data for this theory.

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