1,199 research outputs found
Deformed dimensional regularization for odd (and even) dimensional theories
I formulate a deformation of the dimensional-regularization technique that is
useful for theories where the common dimensional regularization does not apply.
The Dirac algebra is not dimensionally continued, to avoid inconsistencies with
the trace of an odd product of gamma matrices in odd dimensions. The
regularization is completed with an evanescent higher-derivative deformation,
which proves to be efficient in practical computations. This technique is
particularly convenient in three dimensions for Chern-Simons gauge fields,
two-component fermions and four-fermion models in the large N limit, eventually
coupled with quantum gravity. Differently from even dimensions, in odd
dimensions it is not always possible to have propagators with fully Lorentz
invariant denominators. The main features of the deformed technique are
illustrated in a set of sample calculations. The regularization is universal,
local, manifestly gauge-invariant and Lorentz invariant in the physical sector
of spacetime. In flat space power-like divergences are set to zero by default.
Infinitely many evanescent operators are automatically dropped.Comment: 27 pages, 3 figures; v2: expanded presentation of some arguments,
IJMP
HyperK\"ahler quotients and N=4 gauge theories in D=2
We consider certain N=4 supersymmetric gauge theories in D=2 coupled to
quaternionic matter multiplets in a minimal way. These theories admit as
effective theories sigma-models on non-trivial HyperK\"ahler manifolds obtained
as HyperK\"ahler quotients. The example of ALE manifolds is discussed. (Based
on a talk given by P. Fr\'e at the F. Gursey Memorial Conference, Istanbul,
June 1994).Comment: 22 pages, Latex, no figure
3-Point Functions in N=4 Yang-Mills
Three-point functions of analytic (chiral primary) operators in N=4
Yang-Mills theory in four dimensions are calculated using the harmonic
superspace formulation of this theory. In the case of the energy-momentum
tensor multiplet anomaly considerations determine the coefficient. Analyticity
in N=2 harmonic superspace is explicitly checked in a two-loop calculation.Comment: This file requires the feynman.tex macro Some references are adde
A stylized model for the continuous double auction
A stylized phenomenological model for the continuous double auction is introduced. This model is equivalent to two uncoupled M/M/1 queues. The conditions for statistical equilibrium (ergodicity) are derived. The results of Monte Carlo simulations are presented on the behaviour of price differences and log-returns
Ergodic transition in a simple model of the continuous double auction
We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen
A three-loop check of the 'a - maximization' in SQCD with adjoint(s)
The 'a - maximization' was introduced by K. Inrtiligator and B. Wecht for
finding anomalous dimensions of chiral superfields at the IR fixed points of
the RG flow. Using known explicit calculations of anomalous dimensions in the
perturbation theory of SQCD (with one or two additional adjoint fields), it is
checked here at the three-loop level.Comment: 5 pages; the title changed, the text improved and expande
Renormalization Group Flows from Five-Dimensional Supergravity
The use of gauged supergravity as a tool in studying the
AdS/CFT correspondence for Yang-Mills theory is reviewed. The
supergravity potential implies a non-trivial, supersymmetric IR fixed point,
and the flow to this fixed point is described in terms of a supergravity kink.
The results agree perfectly with earlier, independent field theory results. A
supergravity inspired -function, and corresponding -theorem is discussed
for general flows, and the simplified form for supersymmetric flows is also
given. Flows along the Coulomb branch of the Yang-Mills theory are also
described from the five-dimensional perspective.Comment: 12 pages, 3 figures; Latex, ioplppt.sty, iopl12.sty, epsf.sty.
Contribution to Strings `9
The Gravity dual of the Non-Perturbative SUSY Yang-Mills Theory
The anomalous Ward identity is derived for SUSY Yang-Mills theories,
which is resulted out of Wrapping of branes on Supersymmetric two cycles.
From the Ward identity One obtains the Witten-Dijkgraaf-Verlinde-Verlinde
equation and hence can solve for the pre-potential. This way one avoids the
problem of enhancon which maligns the non-perturbative behaviour of the
Yang-Mills theory resulted out of Wrapped branes.Comment: 4 pages, LaTeX. Talk given at the IXth International Symposium on
Particles, Strings and Cosmology PASCOS '03, Mumbai-India, January 3-8 2003.
v2:some reference adde
N=4 Versus N=2 Phases, Hyperk\"Ahler Quotients and the 2D Topological Twist
We consider N=2 and N=4 supersymmetric gauge theories in two-dimensions,
coupled to matter multiplets. In analogy with the N=2 case also in the N=4 case
one can introduce Fayet-Iliopoulos terms.The associated three-parameters have
the meaning of momentum-map levels in a HyperK\"ahler quotient construction.
Differently from the N=2 case, however, the N=4 has a single phase
corresponding to an effective -model. There is no Landau-Ginzburg
phase. The main possible application of our N=4 model is to an effective
Lagrangian construction of a -model on ALE-manifolds. We discuss the A
and B topological twists of these models clarifying some issues not yet
discussed in the literature, in particular the identification of the
topological systems emerging from the twist. Applying our results to the case
of ALE-manifolds we indicate how one can use the topologically twisted theories
to study the K\"ahler class and complex structure deformations of these
gravitational instantons.Comment: plain Latex, 77 pages, SISSA/151/93/E
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