772 research outputs found

### Chiral Rings, Vacua and Gaugino Condensation of Supersymmetric Gauge Theories

We find the complete chiral ring relations of the supersymmetric U(N) gauge
theories with matter in adjoint representation. We demonstrate exact
correspondence between the solutions of the chiral ring and the supersymmetric
vacua of the gauge theory. The chiral ring determines the expectation values of
chiral operators and the low energy gauge group. All the vacua have nonzero
gaugino condensation. We study the chiral ring relations obeyed by the gaugino
condensate. These relations are generalizations of the formula
$S^N=\Lambda^{3N}$ of the pure ${\cal N} =1$ gauge theory.Comment: 38 page

### Extending the Veneziano-Yankielowicz Effective Theory

We extend the Veneziano Yankielowicz (VY) effective theory in order to
account for ordinary glueball states. We propose a new form of the
superpotential including a chiral superfield for the glueball degrees of
freedom. When integrating it ``out'' we obtain the VY superpotential while the
N vacua of the theory naturally emerge. This fact has a counterpart in the
Dijkgraaf and Vafa geometric approach. We suggest a link of the new field with
the underlying degrees of freedom which allows us to integrate it ``in'' the VY
theory. We finally break supersymmetry by adding a gluino mass and show that
the Kahler independent part of the ``potential'' has the same form of the
ordinary Yang-Mills glueball effective potential.Comment: LaTeX, 20 page

### On the Geometry of Matrix Models for N=1*

We investigate the geometry of the matrix model associated with an N=1 super
Yang-Mills theory with three adjoint fields, which is a massive deformation of
N=4. We study in particular the Riemann surface underlying solutions with
arbitrary number of cuts. We show that an interesting geometrical structure
emerges where the Riemann surface is related on-shell to the Donagi-Witten
spectral curve. We explicitly identify the quantum field theory resolvents in
terms of geometrical data on the surface.Comment: 17 pages, 2 figures. v2: reference adde

### On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes

We examine factorisation in the connected prescription of Yang-Mills
amplitudes. The multi-particle pole is interpreted as coming from representing
delta functions as meromorphic functions. However, a naive evaluation does not
give a correct result. We give a simple prescription for the integration
contour which does give the correct result. We verify this prescription for a
family of gauge-fixing conditions.Comment: 16 pages, 1 figur

### Dual Interpretations of Seiberg-Witten and Dijkgraaf-Vafa curves

We give dual interpretations of Seiberg-Witten and Dijkgraaf-Vafa (or matrix
model) curves in n=1 supersymmetric U(N) gauge theory. This duality
interchanges the rank of the gauge group with the degree of the superpotential;
moreover, the constraint of having at most log-normalizable deformations of the
geometry is mapped to a constraint in the number of flavors N_f < N in the dual
theory.Comment: Latex2e, 22 pages, 2 figure

### Chiral Rings, Anomalies and Electric-Magnetic Duality

We study electric-magnetic duality in the chiral ring of a supersymmetric
U(N_c) gauge theory with adjoint and fundamental matter, in presence of a
general confining phase superpotential for the adjoint and the mesons. We find
the magnetic solution corresponding to both the pseudoconfining and higgs
electric vacua. By means of the Dijkgraaf-Vafa method, we match the effective
glueball superpotentials and show that in some cases duality works exactly
offshell. We give also a picture of the analytic structure of the resolvents in
the magnetic theory, as we smoothly interpolate between different higgs vacua
on the electric side.Comment: 54 pages, harvmac. v2: typos correcte

### Quivers via anomaly chains

We study quivers in the context of matrix models. We introduce chains of
generalized Konishi anomalies to write the quadratic and cubic equations that
constrain the resolvents of general affine and non-affine quiver gauge
theories, and give a procedure to calculate all higher-order relations. For
these theories we also evaluate, as functions of the resolvents, VEV's of
chiral operators with two and four bifundamental insertions. As an example of
the general procedure we explicitly consider the two simplest quivers A2 and
A1(affine), obtaining in the first case a cubic algebraic curve, and for the
affine theory the same equation as that of U(N) theories with adjoint matter,
successfully reproducing the RG cascade result.Comment: 32 pages, latex; typos corrected, published versio

### On Tree Amplitudes in Gauge Theory and Gravity

The BCFW recursion relations provide a powerful way to compute tree
amplitudes in gauge theories and gravity, but only hold if some amplitudes
vanish when two of the momenta are taken to infinity in a particular complex
direction. This is a very surprising property, since individual Feynman
diagrams all diverge at infinite momentum. In this paper we give a simple
physical understanding of amplitudes in this limit, which corresponds to a hard
particle with (complex) light-like momentum moving in a soft background, and
can be conveniently studied using the background field method exploiting
background light-cone gauge. An important role is played by enhanced spin
symmetries at infinite momentum--a single copy of a "Lorentz" group for gauge
theory and two copies for gravity--which together with Ward identities give a
systematic expansion for amplitudes at large momentum. We use this to study
tree amplitudes in a wide variety of theories, and in particular demonstrate
that certain pure gauge and gravity amplitudes do vanish at infinity. Thus the
BCFW recursion relations can be used to compute completely general gluon and
graviton tree amplitudes in any number of dimensions. We briefly comment on the
implications of these results for computing massive 4D amplitudes by KK
reduction, as well understanding the unexpected cancelations that have recently
been found in loop-level gravity amplitudes.Comment: 22 pages, 3 figure

### The Proof of the Dijkgraaf-Vafa Conjecture and application to the mass gap and confinement problems

Using generalized Konishi anomaly equations, it is known that one can
express, in a large class of supersymmetric gauge theories, all the chiral
operators expectation values in terms of a finite number of a priori arbitrary
constants. We show that these constants are fully determined by the requirement
of gauge invariance and an additional anomaly equation. The constraints so
obtained turn out to be equivalent to the extremization of the Dijkgraaf-Vafa
quantum glueball superpotential, with all terms (including the
Veneziano-Yankielowicz part) unambiguously fixed. As an application, we fill
non-trivial gaps in existing derivations of the mass gap and confinement
properties in super Yang-Mills theories.Comment: 31 pages, 1 figure; v2: typos corrected; references, a note on
Kovner-Shifman vacua (section 4.3) and a few clarifying comments in Section 3
added; v3: cosmetic changes, JHEP versio

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