skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Bootstrapping 3D fermions

Abstract

We study the conformal bootstrap for a 4-point function of fermions in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge CT. We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N. Finally, we also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.

Authors:
 [1];  [2];  [2];  [1];  [3];  [1]
  1. Princeton Univ., NJ (United States). Joseph Henry Lab.
  2. Yale Univ., New Haven, CT (United States). Dept. of Physics
  3. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States); Princeton Univ., NJ (United States); Yale Univ., New Haven, CT (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1326984
Grant/Contract Number:  
SC0009988; PHY-1418069; PHY-1350180; PHY-1066293
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conformal and W symmetry; nonperturbative effects

Citation Formats

Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., Simmons-Duffin, David, and Yacoby, Ran. Bootstrapping 3D fermions. United States: N. p., 2016. Web. doi:10.1007/JHEP03(2016)120.
Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., Simmons-Duffin, David, & Yacoby, Ran. Bootstrapping 3D fermions. United States. doi:10.1007/JHEP03(2016)120.
Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., Simmons-Duffin, David, and Yacoby, Ran. Thu . "Bootstrapping 3D fermions". United States. doi:10.1007/JHEP03(2016)120. https://www.osti.gov/servlets/purl/1326984.
@article{osti_1326984,
title = {Bootstrapping 3D fermions},
author = {Iliesiu, Luca and Kos, Filip and Poland, David and Pufu, Silviu S. and Simmons-Duffin, David and Yacoby, Ran},
abstractNote = {We study the conformal bootstrap for a 4-point function of fermions in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge CT. We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N. Finally, we also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.},
doi = {10.1007/JHEP03(2016)120},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2016,
place = {United States},
year = {2016},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 38 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973


Duality in quantum field theory
journal, February 1977


Bounding scalar operator dimensions in 4 D CFT
journal, December 2008


Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents
journal, June 2014

  • El-Showk, Sheer; Paulos, Miguel F.; Poland, David
  • Journal of Statistical Physics, Vol. 157, Issue 4-5
  • DOI: 10.1007/s10955-014-1042-7

Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 11
  • DOI: 10.1007/JHEP11(2014)109

A semidefinite program solver for the conformal bootstrap
journal, June 2015


Bootstrapping the O(N ) vector models
journal, June 2014

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)091

Bootstrapping the O(N) archipelago
journal, November 2015

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)106

N = 4 Superconformal Bootstrap
journal, August 2013


Bounds on N $$ \mathcal{N} $$ = 1 superconformal theories with global symmetries
journal, August 2014

  • Berkooz, Micha; Yacoby, Ran; Zait, Amir
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)008

The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions
journal, September 2014

  • Chester, Shai M.; Lee, Jaehoon; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)143

Exact correlators of BPS Operators from the 3d superconformal bootstrap
journal, March 2015

  • Chester, Shai M.; Lee, Jaehoon; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)130

Spinning conformal blocks
journal, November 2011

  • Costa, Miguel S.; Penedones, João; Poland, David
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)154

A note on CFT correlators in three dimensions
journal, July 2013

  • Giombi, Simone; Prakash, Shiroman; Yin, Xi
  • Journal of High Energy Physics, Vol. 2013, Issue 7
  • DOI: 10.1007/JHEP07(2013)105

Spinning conformal correlators
journal, November 2011

  • Costa, Miguel S.; Penedones, João; Poland, David
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)071

Self-organized criticality: An explanation of the 1/ f noise
journal, July 1987


Self-organized criticality
journal, July 1988


Wave Equations in Conformal Space
journal, April 1936

  • Dirac, P. A. M.
  • The Annals of Mathematics, Vol. 37, Issue 2
  • DOI: 10.2307/1968455

Finite-component field representations of the conformal group
journal, June 1969


Projectors, shadows, and conformal blocks
journal, April 2014


Conformal correlators of mixed-symmetry tensors
journal, February 2015


General three-point functions in 4D CFT
journal, January 2015

  • Elkhidir, Emtinan; Karateev, Denis; Serone, Marco
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/JHEP01(2015)133

Deconstructing conformal blocks in 4D CFT
journal, August 2015

  • Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)101

Superembedding methods for 4d -extended SCFTs
journal, November 2012


Conformally compactified Minkowski superspaces revisited
journal, October 2012


Covariant approaches to superconformal blocks
journal, August 2014

  • Fitzpatrick, A. Liam; Kaplan, Jared; Khandker, Zuhair U.
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)129

Manifestly conformal covariant operator-product expansion
journal, December 1971

  • Ferrara, S.; Grillo, A. F.; Gatto, R.
  • Lettere Al Nuovo Cimento Series 2, Vol. 2, Issue 26
  • DOI: 10.1007/BF02770435

Covariant expansion of the conformal four -point function
journal, December 1972


Analyticity properties and asymptotic expansions of conformal covariant Green's functions
journal, February 1974

  • Ferrara, S.; Grillo, A. F.; Gatto, R.
  • Il Nuovo Cimento A, Vol. 19, Issue 4
  • DOI: 10.1007/BF02813413

Properties of partial-wave amplitudes in conformal invariant field theories
journal, April 1975

  • Ferrara, S.; Gatto, R.; Grillo, A. F.
  • Il Nuovo Cimento A, Vol. 26, Issue 3
  • DOI: 10.1007/BF02769009

Conformal four point functions and the operator product expansion
journal, April 2001


Conformal partial waves and the operator product expansion
journal, February 2004


Conformal blocks in the large D limit
journal, August 2013

  • Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David
  • Journal of High Energy Physics, Vol. 2013, Issue 8
  • DOI: 10.1007/JHEP08(2013)107

N $$ \mathcal{N} $$ = 1 superconformal blocks for general scalar operators
journal, August 2014

  • Khandker, Zuhair U.; Li, Daliang; Poland, David
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)049

Quantum field theory in the large N limit: a review
journal, October 2003


Anomalous mass dimension at O(1/N2) in the O(N) Gross-Neveu model
journal, December 1992


COMPUTATION OF CRITICAL EXPONENT η AT O(1/N 3 ) IN THE FOUR-FERMI MODEL IN ARBITRARY DIMENSIONS
journal, February 1994


Operator product expansions and consistency relations in a O(N) invariant fermionic CFT for 2 < d < 4
journal, December 1996


Emergent Space-Time Supersymmetry at the Boundary of a Topological Phase
journal, April 2014


Bootstrapping the Three Dimensional Supersymmetric Ising Model
journal, July 2015


Accidental symmetries and the conformal bootstrap
journal, January 2016

  • Chester, Shai M.; Giombi, Simone; Iliesiu, Luca V.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)110

Perturbative search for dead-end CFTs
journal, May 2015


Bounds on 4D conformal and superconformal field theories
journal, May 2011

  • Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)017

Carving out the space of 4D CFTs
journal, May 2012

  • Poland, David; Simmons-Duffin, David; Vichi, Alessandro
  • Journal of High Energy Physics, Vol. 2012, Issue 5
  • DOI: 10.1007/JHEP05(2012)110

Conformal Field Theories in Fractional Dimensions
journal, April 2014