Truncated conformal space approach in d dimensions: A cheap alternative to lattice field theory?

Hogevorst, M.; Rychkov, S.; van Rees, B.C.

Abstract

We show how to perform accurate, nonperturbative and controlled calculations in quantum field theory in d dimensions. We use the truncated conformal space approach, a Hamiltonian method which exploits the conformal structure of the UV fixed point. The theory is regulated in the IR by putting it on a sphere of a large finite radius. The quantum field theory Hamiltonian is expressed as a matrix in the Hilbert space of conformal field theory states. After restricting ourselves to energies below a certain UV cutoff, an approximation to the spectrum is obtained by numerical diagonalization of the resulting finite-dimensional matrix. The cutoff dependence of the results can be computed and efficiently reduced via a renormalization procedure. We work out the details of the method for the ϕ4 theory in d dimensions with d being not necessarily integer. A numerical analysis is then performed for the specific case d=2.5, a value chosen in the range where UV divergences are absent. By going from weak to intermediate to strong coupling, we are able to observe the symmetry-preserving, symmetry-breaking, and conformal phases of the theory, and perform rough measurements of masses and critical exponents. As a byproduct of our investigations we find that both the free and the interacting theories in nonintegral d are not unitary, which however does not seem to cause much effect at low energies.

Citation

Hogevorst, M., Rychkov, S., & van Rees, B. (2015). Truncated conformal space approach in d dimensions: A cheap alternative to lattice field theory?. Physical Review D, 91(2), Article 025005. https://doi.org/10.1103/physrevd.91.025005

• Journal Article Type: Article
• Acceptance Date: Jan 6, 2015
• Publication Date: Jan 6, 2015
• Deposit Date: Dec 30, 2015
• Publicly Available Date: Jan 25, 2016
• Journal: Physical Review D - Particles, Fields, Gravitation, and Cosmology
• Print ISSN: 1550-7998
• Electronic ISSN: 1550-2368
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 91
• Issue: 2
• Article Number: 025005
• DOI: https://doi.org/10.1103/physrevd.91.025005
• Public URL: https://durham-repository.worktribe.com/output/1416156
• Related Public URLs: http://arxiv.org/abs/1409.1581