32,374 research outputs found
A scaling theory for the long-range to short-range crossover and an infrared duality
We study the second-order phase transition in the -dimensional Ising model
with long-range interactions decreasing as a power of the distance .
For below some known value , the transition is described by a
conformal field theory without a local stress tensor operator, with critical
exponents varying continuously as functions of . At , the phase
transition crosses over to the short-range universality class. While the
location of this crossover has been known for 40 years, its physics has
not been fully understood, the main difficulty being that the standard
description of the long-range critical point is strongly coupled at the
crossover. In this paper we propose another field-theoretic description which,
on the contrary, is weakly coupled near the crossover. We use this description
to clarify the nature of the crossover and make predictions about the critical
exponents. That the same long-range critical point can be reached from two
different UV descriptions provides a new example of infrared duality.Comment: 57pp, detailed version of arXiv:1703.03430, v2: misprints corrected,
v3: refs and discussion of log corrections at the crossover added, v4:
published version plus extra comments in appendix A,B and an acknowledgement,
v5: published version plus extra comments in appendix A,B and an
acknowledgement (replacing the wrong tex file of v4
Renormalization of a class of non-renormalizable theories
Certain power-counting non-renormalizable theories, including the most
general self-interacting scalar fields in four and three dimensions and
fermions in two dimensions, have a simplified renormalization structure. For
example, in four-dimensional scalar theories, 2n derivatives of the fields,
n>1, do not appear before the nth loop. A new kind of expansion can be defined
to treat functions of the fields (but not of their derivatives)
non-perturbatively. I study the conditions under which these theories can be
consistently renormalized with a reduced, eventually finite, set of independent
couplings. I find that in common models the number of couplings sporadically
grows together with the order of the expansion, but the growth is slow and a
reasonably small number of couplings is sufficient to make predictions up to
very high orders. Various examples are solved explicitly at one and two loops.Comment: 38 pages, 1 figure; v2: more explanatory comments and references;
appeared in JHE
Higher derivatives and brane-localised kinetic terms in gauge theories on orbifolds
We perform a detailed analysis of one-loop corrections to the self-energy of
the (off-shell) gauge bosons in six-dimensional N=1 supersymmetric gauge
theories on orbifolds. After discussing the Abelian case in the standard
Feynman diagram approach, we extend the analysis to the non-Abelian case by
employing the method of an orbifold-compatible one-loop effective action for a
classical background gauge field. We find that bulk higher derivative and
brane-localised gauge kinetic terms are required to cancel one-loop divergences
of the gauge boson self energy. After their renormalisation we study the
momentum dependence of both the higher derivative coupling h(k^2) and the {\it
effective} gauge coupling g_eff(k^2). For momenta smaller than the
compactification scales, we obtain the 4D logarithmic running of g_eff(k^2),
with suppressed power-like corrections, while the higher derivative coupling is
constant. We present in detail the threshold corrections to the low energy
gauge coupling, due to the massive bulk modes. At momentum scales above the
compactification scales, the higher derivative operator becomes important and
leads to a power-like running of g_eff(k^2) with respect to the momentum scale.
The coefficient of this running is at all scales equal to the renormalised
coupling of the higher derivative operator which ensures the quantum
consistency of the model. We discuss the relation to the similar one-loop
correction in the heterotic string, to show that the higher derivative
operators are relevant in that case too, since the field theory limit of the
one-loop string correction does not commute with the infrared regularisation of
the (on-shell) string result.Comment: 1+45 pages, 2 figures, JHEP style file, version to be published in
JHE
Effective Beta-Functions for Effective Field Theory
We consider the problem of determining the beta-functions for any reduced
effective field theory. Even though not all the Green's functions of a reduced
effective field theory are renormalizable, unlike the full effective field
theory, certain effective beta- functions for the reduced set of couplings may
be calculated without having to introduce vertices in the Feynman rules for
redundant operators. These effective beta-functions suffice to apply the
renormalization group equation to any transition amplitude (i.e., S- matrix
element), thereby rendering reduced effective field theories no more cumbersome
than traditionally renormalizable field theories. These effective
beta-functions may equally be regarded as the running of couplings for a
particular redefinition of the fields.Comment: 13 pages, LaTeX (requires JHEP class). Version 3: additional
references and a slight expansion of Sections 3 and 5. No substantive change
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