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 Web site:||http://dx.doi.org/10.1103/PhysRevD.91.025005|
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|Record Created:||25 Jan 2016 11:20|
|Last Modified:||25 Jan 2016 11:42|
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