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

Hogevorst, M. and Rychkov, S. and van Rees, B.C. (2015) 'Truncated conformal space approach in d dimensions : a cheap alternative to lattice field theory?', Physical review D., 91 (2). 025005.


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.

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Publisher statement:Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Record Created:25 Jan 2016 11:20
Last Modified:25 Jan 2016 11:42

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