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Title: Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion

Authors:
; ; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1343350
Grant/Contract Number:
SC0010255
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 118; Journal Issue: 6; Related Information: CHORUS Timestamp: 2017-02-09 22:08:26; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Gliozzi, Ferdinando, Guerrieri, Andrea L., Petkou, Anastasios C., and Wen, Congkao. Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion. United States: N. p., 2017. Web. doi:10.1103/PhysRevLett.118.061601.
Gliozzi, Ferdinando, Guerrieri, Andrea L., Petkou, Anastasios C., & Wen, Congkao. Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion. United States. doi:10.1103/PhysRevLett.118.061601.
Gliozzi, Ferdinando, Guerrieri, Andrea L., Petkou, Anastasios C., and Wen, Congkao. Thu . "Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion". United States. doi:10.1103/PhysRevLett.118.061601.
@article{osti_1343350,
title = {Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion},
author = {Gliozzi, Ferdinando and Guerrieri, Andrea L. and Petkou, Anastasios C. and Wen, Congkao},
abstractNote = {},
doi = {10.1103/PhysRevLett.118.061601},
journal = {Physical Review Letters},
number = 6,
volume = 118,
place = {United States},
year = {Thu Feb 09 00:00:00 EST 2017},
month = {Thu Feb 09 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevLett.118.061601

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  • Here, we describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We also compute, to the first non-trivial order in the ε-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O(N)-invariant theories, as well as theories with multiple deformations. When availablemore » we agree with older results, but we also produce a wealth of new ones. Furthermore, unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.« less
  • The operator product expansion for {open_quotes}small{close_quotes} Wilson loops in N=4, d=4 SYM theory is studied. The OPE coefficients are calculated in the large {ital N} and g{sub YM}{sup 2}N limit by exploiting the AdS-CFT correspondence. We also consider Wilson surfaces in the (0,2), d=6 superconformal theory. In this case, we find that the UV divergent terms include a term proportional to the rigid string action. {copyright} {ital 1999} {ital The American Physical Society}
  • An expansion of the type < phi (x$sub 1$)...phi (x/subn/) > $sub 0$ = < phi (x$sub 1$) phi (x$sub 2$) > $sub 0$ < phi (x$sub 3$)...phi (x/subn/) > $sub 0$ + $Sigma$/sub chi/l C$sup 2$(chi/subl/) $Integral$ (dp) Q/sup chi/l (x$sub 1$,x$sub 2$;-p) w/sub chi/l(p) Q/sup chi//subl/(p;x$sub 3$,... x/subn/) is derived, where chi/subl/ = l,c/subl/ are labels for infinite-dimensional symmetric tensor representations of the Euclidean conformal group O/sup arrow-up/ (2h + 1, 1), X$sub 1$ = 1, -c/subl/, the constants C (x/subl/) are real, and Q/ sup chi/ and w/sub chi/ have the properties of vacuum expectation values ofmore » field products. The starting point is an infinite set of coupled nonlinear integral equations for Euclidean Green's functions in 2h space-time dimensions of the type written some 15 years ago by Fradkin and Symanzik. The Green's functions of the corresponding Gell-Mann--Low limit theory are expanded in conformal partial waves. The dynamical equations imply the existence of poles and factorization of residues in the partial waves as functions of the representation parameters. In proving the validity of the expansion, use is made of some differential relations between partially equivalent exceptional representations O/sup arrow-up/(2h + 1, 1), established in an earlier paper. This work completes the group-theoretical derivation of the vacuum operator-product expansion undertaken by Mack in 1973. (AIP)« less