A conformal truncation framework for infinite-volume dynamics

Katz, Emanuel; Khandker, Zuhair U.; Walters, Matthew T.

doi:10.1007/JHEP07(2016)140

Title: A conformal truncation framework for infinite-volume dynamics

Journal Article · 27 July 2016 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP07(2016)140 · OSTI ID:1358561

Katz, Emanuel ^[1]; Khandker, Zuhair U. ^[2]; Walters, Matthew T. ^[2]

Boston Univ., Boston, MA (United States). Dept. of Physics; University of Illinois
Boston Univ., Boston, MA (United States). Dept. of Physics

Here, we present a new framework for studying conformal field theories deformed by one or more relevant operators. The original CFT is described in infinite volume using a basis of states with definite momentum, P, and conformal Casimir, C. The relevant deformation is then considered using lightcone quantization, with the resulting Hamiltonian expressed in terms of this CFT basis. Truncating to states with C ≤ C_max, one can numerically find the resulting spectrum, as well as other dynamical quantities, such as spectral densities of operators. This method requires the introduction of an appropriate regulator, which can be chosen to preserve the conformal structure of the basis. We check this framework in three dimensions for various perturbative deformations of a free scalar CFT, and for the case of a free O(N) CFT deformed by a mass term and a non-perturbative quartic interaction at large-N. In all cases, the truncation scheme correctly reproduces known analytic results. As a result, we also discuss a general procedure for generating a basis of Casimir eigenstates for a free CFT in any number of dimensions.

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Research Organization:: Boston Univ., Boston, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF)

Grant/Contract Number:: SC0010025

OSTI ID:: 1358561

Alternate ID(s):: OSTI ID: 22610308

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 7 Vol. 2016; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Numerical Renormalization Group for Continuum One-Dimensional Systems Konik, Robert M.; Adamov, Yury Physical Review Letters, Vol. 98, Issue 14 https://doi.org/10.1103/physrevlett.98.147205	journal	April 2007
Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories Coser, Andrea; Beria, Marco; Brandino, Giuseppe arXiv https://doi.org/10.48550/arxiv.1409.1494	text	January 2014
Effective conformal theory and the flat-space limit of AdS Fitzpatrick, A. Liam; Katz, Emanuel; Poland, David Journal of High Energy Physics, Vol. 2011, Issue 7 https://doi.org/10.1007/jhep07(2011)023	journal	July 2011
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevE.50.888	journal	August 1994
On the renormalisation group for the boundary truncated conformal space approach Watts, Gérard M. T. Nuclear Physics B, Vol. 859, Issue 2 https://doi.org/10.1016/j.nuclphysb.2012.01.012	journal	June 2012
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Quantum field theory on lightlike slabs Leutwyler, H.; Klauder, J. R.; Streit, L. Il Nuovo Cimento A, Vol. 66, Issue 3 https://doi.org/10.1007/BF02826338	journal	April 1970
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Confinement in the q-state Potts model: an RG-TCSA study Lencsés, M.; Takács, G. Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/jhep09(2015)146	journal	September 2015
Critical exponents of the 3d Ising and related models from Conformal Bootstrap Gliozzi, Ferdinando; Rago, Antonio arXiv https://doi.org/10.48550/arxiv.1403.6003	text	January 2014
Large N field theories, string theory and gravity Aharony, Ofer; Gubser, Steven S.; Maldacena, Juan Physics Reports, Vol. 323, Issue 3-4 https://doi.org/10.1016/s0370-1573(99)00083-6	journal	January 2000
Nonperturbative study of the two-frequency sine-Gordon model Bajnok, Z.; Palla, L.; Takács, G. Nuclear Physics B, Vol. 601, Issue 3 https://doi.org/10.1016/s0550-3213(01)00067-0	journal	May 2001
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/physreve.50.888	journal	August 1994
Confinement in the q-state Potts model: an RG-TCSA study Lencses, M.; Takacs, G. arXiv https://doi.org/10.48550/arxiv.1506.06477	text	January 2015
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Introduction to stochastic error correction methods Lee, Dean; Salwen, Nathan; Windoloski, Mark Physics Letters B, Vol. 502, Issue 1-4 https://doi.org/10.1016/S0370-2693(01)00198-8	journal	March 2001

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Title: A conformal truncation framework for infinite-volume dynamics

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