2014/09/30 by Matthijs Hogervorst, Slava Rychkov, Balt C. van Rees · 1 citation
Physics and Astronomy · #hep-th #cond-mat.stat-mech #cond-mat.str-el #hep-lat #hep-ph
paper · pdf · doi:10.1103/physrevd.91.025005
published as Phys. Rev. D 91, 025005 (2015) · 56 pages, 22 figures; V2: defective figure file replaced; V3: minor corrections; refs added; V4: refs updated
arxiv created 2015/12/03 · arxiv updated 2015/12/04
We show how to perform accurate, nonperturbative and controlled calculations in quantum field theory in d dimensions. We use the Truncated Conformal Space Approach (TCSA), 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 QFT Hamiltonian is expressed as a matrix in the Hilbert space of CFT 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 phi4 theory in d dimensions with d 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 non integral d are not unitary, which however does not seem to cause much effect at low energies.