3,116 research outputs found
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
Chiral Rings of Deconstructive [SU(n_c)]^N Quivers
Dimensional deconstruction of 5D SQCD with general n_c, n_f and k_CS gives
rise to 4D N=1 gauge theories with large quivers of SU(n_c) gauge factors. We
construct the chiral rings of such [SU(n_c)]^N theories, off-shell and
on-shell. Our results are broadly similar to the chiral rings of single U(n_c)
theories with both adjoint and fundamental matter, but there are also some
noteworthy differences such as nonlocal meson-like operators where the quark
and antiquark fields belong to different nodes of the quiver. And because our
gauge groups are SU(n_c) rather than U(n_c), our chiral rings also contain a
whole zoo of baryonic and antibaryonic operators.Comment: 93 pages, LaTeX, PSTricks macros; 1 reference added in v
Classical/quantum integrability in AdS/CFT
We discuss the AdS/CFT duality from the perspective of integrable systems and
establish a direct relationship between the dimension of single trace local
operators composed of two types of scalar fields in N=4 super Yang-Mills and
the energy of their dual semiclassical string states in AdS(5) X S(5). The
anomalous dimensions can be computed using a set of Bethe equations, which for
``long'' operators reduces to a Riemann-Hilbert problem. We develop a unified
approach to the long wavelength Bethe equations, the classical ferromagnet and
the classical string solutions in the SU(2) sector and present a general
solution, governed by complex curves endowed with meromorphic differentials
with integer periods. Using this solution we compute the anomalous dimensions
of these long operators up to two loops and demonstrate that they agree with
string-theory predictions.Comment: 49 pages, 5 figures, LaTeX; v2: complete proof of the two-loop
equivalence between the sigma model and the gauge theory is added. References
added; v4,v5,v6: misprints correcte
The Fourier transform and convolutions generated by a differential operator with boundary condition on a segment
We introduce the concepts of the Fourier transform and convolution generated
by an arbitrary restriction of the differentiation operator in the space
In contrast to the classical convolution, the introduced
convolution explicitly depends on the boundary condition that defines the
domain of the operator The convolution is closely connected to the inverse
operator or to the resolvent. So, we first find a representation for the
resolvent, and then introduce the required convolution.Comment: 15 page
Classical integrability in the BTZ black hole
Using the fact the BTZ black hole is a quotient of AdS_3 we show that
classical string propagation in the BTZ background is integrable. We construct
the flat connection and its monodromy matrix which generates the non-local
charges. From examining the general behaviour of the eigen values of the
monodromy matrix we determine the set of integral equations which constrain
them. These equations imply that each classical solution is characterized by a
density function in the complex plane. For classical solutions which correspond
to geodesics and winding strings we solve for the eigen values of the monodromy
matrix explicitly and show that geodesics correspond to zero density in the
complex plane. We solve the integral equations for BMN and magnon like
solutions and obtain their dispersion relation. Finally we show that the set of
integral equations which constrain the eigen values of the monodromy matrix can
be identified with the continuum limit of the Bethe equations of a twisted
SL(2, R) spin chain at one loop.Comment: 45 pages, Reference added, typos corrected, discussion on geodesics
improved to include all geodesic
Universality of Nonperturbative Effect in Type 0 String Theory
We derive the nonperturbative effect in type 0B string theory, which is
defined by taking the double scaling limit of a one-matrix model with a two-cut
eigenvalue distribution. However, the string equation thus derived cannot
determine the nonperturbative effect completely, at least without specifying
unknown boundary conditions. The nonperturbative contribution to the free
energy comes from instantons in such models. We determine by direct computation
in the matrix model an overall factor of the instanton contribution, which
cannot be determined by the string equation itself. We prove that it is
universal in the sense that it is independent of the detailed structure of
potentials in the matrix model. It turns out to be a purely imaginary number
and therefore can be interpreted as a quantity related to instability of the
D-brane in type 0 string theory. We also comment on a relation between our
result and boundary conditions for the string equation.Comment: 26 pages, LaTe
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