83 research outputs found
Renormalization of Supersymmetric QCD on the Lattice
We perform a pilot study of the perturbative renormalization of a
Supersymmetric gauge theory with matter fields on the lattice. As a specific
example, we consider Supersymmetric QCD (SQCD). We study the
self-energies of all particles which appear in this theory, as well as the
renormalization of the coupling constant. To this end we compute,
perturbatively to one-loop, the relevant two-point and three-point Green's
functions using both dimensional and lattice regularizations. Our lattice
formulation involves the Wilson discretization for the gluino and quark fields;
for gluons we employ the Wilson gauge action; for scalar fields (squarks) we
use naive discretization. The gauge group that we consider is , while
the number of colors, , the number of flavors, , and the gauge
parameter, , are left unspecified.
We obtain analytic expressions for the renormalization factors of the
coupling constant () and of the quark (), gluon (), gluino
(), squark (), and ghost () fields on the lattice.
We also compute the critical values of the gluino, quark and squark masses.
Finally, we address the mixing which occurs among squark degrees of freedom
beyond tree level: we calculate the corresponding mixing matrix which is
necessary in order to disentangle the components of the squark field via an
additional finite renormalization.Comment: 8 pages, 6 figures, Lattice 201
Off-equilibrium scaling behaviors across first-order transitions
We study off-equilibrium behaviors at first-order transitions (FOTs) driven
by a time dependence of the temperature across the transition point Tc, such as
the linear behavior T(t)/Tc = 1 - t/ts where ts is a time scale. In particular,
we investigate the possibility of nontrivial off-equilibrium scaling behaviors
in the regime of slow changes, corresponding to large ts, analogous to those
arising at continuous transitions, which lead to the so-called Kibble-Zurek
mechanism.
We consider the 2D Potts models which provide an ideal theoretical laboratory
to investigate issues related to FOTs driven by thermal fluctuations. We put
forward general ansatzes for off-equilibrium scaling behaviors around the time
t=0 corresponding to Tc. Then we present numerical results for the q=10 and
q=20 Potts models. We show that phenomena analogous to the Kibble-Zurek
off-equilibrium scaling emerge also at FOTs with relaxational dynamics, when
appropriate boundary conditions are considered, such as mixed boundary
conditions favoring different phases at the opposite sides of the system, which
enforce an interface in the system.Comment: 11 pages, some more ref
Anomalous finite-size scaling at thermal first-order transitions in systems with disordered boundary conditions
We investigate the equilibrium and off-equilibrium behaviors of systems at
thermal first-order transitions (FOTs) when the boundary conditions favor one
of the two phases. As a theoretical laboratory we consider the two-dimensional
Potts model. We show that an anomalous finite-size scaling emerges in systems
with open boundary conditions favoring the disordered phase, associated with a
mixed regime where the two phases are spatially separated. Correspondingly, if
the system is slowly heated across the transition, the characteristic times of
the off-equilibrium dynamics scale with a power of the size. We argue that
these features generally apply to systems at FOTs, when boundary conditions
favor one of the two phases. In particular, they should be relevant for the
experimental search of FOTs of the quark-gluon plasma in heavy-ion collisions.Comment: 5 page
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