142,940 research outputs found

### Do the gravitational corrections to the beta functions of the quartic and Yukawa couplings have an intrinsic physical meaning?

We study the beta functions of the quartic and Yukawa couplings of General
Relativity and Unimodular Gravity coupled to the $\lambda\phi^4$ and Yukawa
theories with masses. We show that the General Relativity corrections to those
beta functions as obtained from the 1PI functional by using the standard MS
multiplicative renormalization scheme of Dimensional Regularization are gauge
dependent and, further, that they can be removed by a non-multiplicative,
though local, field redefinition. An analogous analysis is carried out when
General Relativity is replaced with Unimodular Gravity. Thus we show that any
claim made about the change in the asymptotic behaviour of the quartic and
Yukawa couplings made by General Relativity and Unimodular Gravity lack
intrinsic physical meaning.Comment: 6 pages, 7 figure

### Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions

We show at one-loop and first order in the noncommutativity parameters that
in any noncommutative GUT inspired theory the total contribution to the
fermionic four point functions coming only from the interaction between
fermions and gauge bosons, though not UV finite by power counting, is UV finite
at the end of the day. We also show that this is at odds with the general case
for noncommutative gauge theories --chiral or otherwise-- defined by means of
Seiberg-Witten maps that are the same --barring the gauge group
representation-- for left-handed spinors as for right-handed spinors. We
believe that the results presented in this paper tilt the scales to the side of
noncommutative GUTS and noncommutative GUT inspired versions of the Standard
Model.Comment: 11 pages, 3 figures. Version 2: references fixed and completed.
Version 3: Comments adde

### The Seiberg-Witten map and supersymmetry

The lack of any local solution to the first-order-in-h omegamn Seiberg-Witten
(SW) map equations for U(1) vector superfields compels us to obtain the most
general solution to those equations that is a quadratic polynomial in the
ordinary vector superfield, v, its chiral and antichiral projections and the
susy covariant derivatives of them all. Furnished with this solution, which is
local in the susy Landau gauge, we construct an ordinary dual of noncommutative
U(1) SYM in terms of ordinary fields which carry a linear representation of the
N=1 susy algebra. By using the standard SW map for the N=1 U(1) gauge
supermultiplet we define an ordinary U(1) gauge theory which is dual to
noncommutative U(1) SYM in the WZ gauge. We show that the ordinary dual so
obtained is supersymmetric, for, as we prove as we go along, the ordinary gauge
and fermion fields that we use to define it carry a nonlinear representation of
the N=1 susy algebra. We finally show that the two ordinary duals of
noncommutative U(1) SYM introduced above are actually the same N=1 susy gauge
theory. We also show in this paper that the standard SW map is never the theta
theta--bar component of a local superfield in v and check that, at least at a
given approximation, a suitable field redefinition of that map makes the
noncommutative and ordinary --in a Bmn field-- susy U(1) DBI actions
equivalent.Comment: 28 pages. No figure

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