Research Interest of Mohammad Edalati

      Publication 1: On singular effective superpotentials in supersymmetric gauge theories (URL)
      Publication 2: Generalized Konishi anomaly, Seiberg duality and singular effective superpotentials (URL)
      Publication 3: Sp(N) higher-derivative F-terms via singular superpotentials (URL)

    URL of Research: 

Statement of Interest:


  My research centers around various aspects of string/M theory and
its connections to gauge theories with various amounts of
supersymmetry. In particular, I am interested in:
 
 1) Time-dependent backgrounds in string/M theory.  In collaboration
with Prof. Sumit Das and Dr. Jeremy Michelson of the University of
Kentucky, I have recently started to work on time-dependent
backgrounds in string/M theory, especially the recent matrix big bang
model of B. Craps, S. Sethi and E. Verlinde. The M-theory lift of the
light-like linear background of type IIA superstring theory is
singular and resembles a big-bang type singularity.

Therefore such a background provides a toy model to study a big bang
in string theory. It turns out that light can be shed on the physics
of the singularity in the sense that the dual matrix description of
the theory, which is a 1+1-dimensional super Yang-Mills on the Milne
orbifold, is free at the time of the big-bang. One can then study the
quantum effects in this matrix theory. In particular, it has been
shown that there exists a one-loop potential which vanishes at the big
bang time. A natural extension of this model would be to construct
similar singular cosmological type solutions in type IIB theory, and
lift them to M-theory to study the physics around the singularity
using the holographic dual description in terms of a matrix super
Yang-Mills theory. We are currently working on such generalizations.
 
 2) AdS/CFT correspondence. In collaboration with my advisor,
Prof. Philip Argyres, and Dr. Justin Vazquez-Poritz, I am currently
investigating the holographic picture of D3-branes on Calabi-Yau
cones. A recently-found countably infinite family of Sasaki-Einstein
spaces form the base of the cone. Although these Sasaki-Einstein
spaces are regular, the corresponding Calabi-Yau cones have a
curvature singularity at the apex. The singularity can be smoothed
out, just for a special case, by deforming the cone and adding
fractional 3-branes, providing a geometrical realization of chiral
symmetry breaking and confinement in the IR regime of the dual gauge
theory. However, this singularity resolution procedure does not work
(past a first-order deformation) for the rest of Sasaki-Einstein base
spaces. We have constructed an alternative method in which the
3-branes are wrapped on a circle which is fibred over a resolved
Calabi-Yau cone. One of the interesting features of our method is that
these wrapped 3-branes provide an infinite number of holographic flows
from a four dimensional N=1 superconformal gauge theory in the UV
limit to a confining N=2 three dimensional gauge theory in the IR
regime [1].
 
 3) Supersymmetric gauge theories and their D-brane realizations. I
have also been working on the superpotentials of N =1 supersymmetric
gauge theories. Despite much progress in these theories, their
effective superpotentials for the case of many flavors have not been
discussed in the literature. This is partly because the effective
superpotentials are singular when expressed in terms of the local
gauge-invariant chiral fields, and a naive analysis shows that they
cannot give the correct description of the moduli space of vacua. We
have shown that the singularities are not actually a problem and the
effective superpotentials must exist, correctly describe the moduli
space of vacua, are consistent under RG flow to fewer flavors upon
turning on masses, and reproduce by a tree-level calculation the
higher-derivative F-terms calculated by C. Beasely and E. Witten using
instanton methods. We have first illustrated the above statements in
the simplest case: four dimensional SU(2) supersymmetric gauge theory
with m massless flavors in the fundamental representation [2]. We have
then generalized our study to higer-rank SU(n) gauge groups. It has
been shown that the generalized Konishi anomaly equations are useful
in determining the effective superpotentials of various N=1
supersymmetric gauge theories. These equations become very complicated
when applied for SU(n) supersymmetric gauge theories with a large
number of flavors. But, we have been able to dramatically simplify
them for m=n+2 flavors. In this case, we have shown that the
generalized Konishi anomaly equations are not integrable to give the
effective superpotential of the theory, in accordance with our general
expectations. Nevertheless, we have derived the effective
superpotential using the Seiberg dual description of the theory
[3]. In a similar vein, we have also considered Sp(n) gauge groups
and, using some consistency checks, have demonstrated that the
singular effective superpotentials are indeed perfectly sensible, as
well [4]. We also noted that perfectly sensible singular effective
superpotentials can also exist in supersymmetric gauge theories in
various dimensions; for example, on the Higgs branch of the three
dimensional N =2 SU(2) supersymmetric gauge theories.
 
 3) Solitons and their D-brane realizations. I am working on another
project exploring supersymmetric gauge theories and string theory:
solitons in supersymmetric gauge theories and their D-brane
realizations, in collaboration with Professor David Tong of Cambridge
University. In particular, we are studying the two dimensional (0, 2)
dynamics of the vortex string worldsheet (heterotic vortex
string). Given the quantitative correspondence between two dimensional
sigma models and four dimensional gauge theories, we are trying to
understand how some aspects of N=1 gauge theories in four dimensions,
like Seiberg duality, appears in two dimensions, and vice versa.
 
 Publications and pre-prints:
 
 [1] P. C. Argyres, M. Edalati and J. Vazquez-Poritz, Orbifolds of
special holonomy and confining gauge theories, to appear soon.
 
 [2] P. C. Argyres and M. Edalati, On singular effective
superpotentials in supersymmetric gauge theories, J. High Energy
Physics. 01 (2006) 012, [hep-th/0510020].
 
 [3] P. C. Argyres and M. Edalati, Generalized Konishi anomaly,
Seiberg duality, and singular effective superpotentials, J. High
Energy Physics. 02 (2006) 071, [hep-th/0511272].
 
 [4] P. C. Argyres and M. Edalati, \Sp(N) higher-derivative F-terms
via singular superpotentials, [hep-th/0603025].
 
 [5] M. Edalati and D. Tong, Heterotic vortex string, to appear soon.