197 research outputs found
Critical Ising Model with Boundary Magnetic Field: RG Interface and Effective Hamiltonians
Critical 2D Ising model with a boundary magnetic field is arguably the
simplest QFT that interpolates between two non-trivial fixed points. We use the
diagonalising Bogolyubov transformation for this model to investigate two
quantities. Firstly we explicitly construct an RG interface operator that is a
boundary condition changing operator linking the free boundary condition with
the one with a boundary magnetic field. We investigate its properties and in
particular show that in the limit of large magnetic field this operator becomes
the dimension 1/16 primary field linking the free and fixed boundary
conditions. Secondly we use Schrieffer-Wolff method to construct effective
Hamiltonians both near the UV and IR fixed points.Comment: 38 pages; v.2 minor changes, to appear in JHE
On Asymptotic Hamiltonian for SU(N) Matrix Theory
We compute the leading contribution to the effective Hamiltonian of SU(N)
matrix theory in the limit of large separation. We work with a gauge fixed
Hamiltonian and use generalized Born-Oppenheimer approximation, extending the
recent work of Halpern and Schwartz for SU(2). The answer turns out to be a
free Hamiltonian for the coordinates along the flat directions of the
potential. Applications to finding ground state candidates and calculation of
the correction (surface) term to Witten index are discussed.Comment: 13 pages, Latex; v2: a reference added; v3: References to the papers
by M.B. Green and M. Gutperle are added. The complete calculation of the
Witten index for SU(N) matrix theory follows from combination of the results
of our paper with the results of M.B. Green and M. Gutperle and the results
obtained by G. Moore, N. Nekrasov, and S. Shatashvil
1/4-BPS states on noncommutative tori
We give an explicit expression for classical 1/4-BPS fields in supersymmetric
Yang-Mills theory on noncommutative tori. We use it to study quantum 1/4-BPS
states. In particular we calculate the degeneracy of 1/4-BPS energy levels.Comment: 15 pages, Latex; v.2 typos correcte
Renormalization group defects for boundary flows
Recently Gaiotto [1] considered conformal defects which produce an expansion
of infrared local fields in terms of the ultraviolet ones for a given
renormalization group flow. In this paper we propose that for a boundary RG
flow in two dimensions there exist boundary condition changing fields (RG
defect fields) linking the UV and the IR conformal boundary conditions which
carry similar information on the expansion of boundary fields at the fixed
points. We propose an expression for a pairing between IR and UV operators in
terms of a four-point function with two insertions of the RG defect fields. For
the boundary flows in minimal models triggered by \psi_{13} perturbation we
make an explicit proposal for the RG defect fields. We check our conjecture by
a number of calculations done for the example of (p,2)--> (p-1,1)+(p+1,1)
flows.Comment: 1+23 pages, 2 Latex figures; v.3: minor corrections throughout the
text, references adde
Compactification of M(atrix) theory on noncommutative toroidal orbifolds
It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative tori
arise naturally in consideration of toroidal compactifications of M(atrix)
theory. A similar analysis of toroidal Z_{2} orbifolds leads to the algebra
B_{\theta} that can be defined as a crossed product of noncommutative torus and
the group Z_{2}. Our paper is devoted to the study of projective modules over
B_{\theta} (Z_{2}-equivariant projective modules over a noncommutative torus).
We analyze the Morita equivalence (duality) for B_{\theta} algebras working out
the two-dimensional case in detail.Comment: 19 pages, Latex; v2: comments clarifying the duality group structure
added, section 5 extended, minor improvements all over the tex
Infrared properties of boundaries in 1-d quantum systems
We present some partial results on the general infrared behavior of
bulk-critical 1-d quantum systems with boundary. We investigate whether the
boundary entropy, s(T), is always bounded below as the temperature T decreases
towards 0, and whether the boundary always becomes critical in the IR limit. We
show that failure of these properties is equivalent to certain seemingly
pathological behaviors far from the boundary. One of our approaches uses real
time methods, in which locality at the boundary is expressed by analyticity in
the frequency. As a preliminary, we use real time methods to prove again that
the boundary beta-function is the gradient of the boundary entropy, which
implies that s(T) decreases with T. The metric on the space of boundary
couplings is interpreted as the renormalized susceptibility matrix of the
boundary, made finite by a natural subtraction.Comment: 26 pages, Late
Gradient formula for the beta-function of 2d quantum field theory
We give a non-perturbative proof of a gradient formula for beta functions of
two-dimensional quantum field theories. The gradient formula has the form
\partial_{i}c = - (g_{ij}+\Delta g_{ij} +b_{ij})\beta^{j} where \beta^{j} are
the beta functions, c and g_{ij} are the Zamolodchikov c-function and metric,
b_{ij} is an antisymmetric tensor introduced by H. Osborn and \Delta g_{ij} is
a certain metric correction. The formula is derived under the assumption of
stress-energy conservation and certain conditions on the infrared behaviour the
most significant of which is the condition that the large distance limit of the
field theory does not exhibit spontaneously broken global conformal symmetry.
Being specialized to non-linear sigma models this formula implies a one-to-one
correspondence between renormalization group fixed points and critical points
of c.Comment: LaTex file, 31 pages, no figures; v.2 referencing corrected in the
introductio
Noncommutative supergeometry, duality and deformations
We introduce a notion of -algebra that can be considered as a
generalization of the notion of -manifold (a supermanifold equipped with an
odd vector field obeying ). We develop the theory of connections on
modules over -algebras and prove a general duality theorem for gauge
theories on such modules. This theorem containing as a simplest case
-duality of gauge theories on noncommutative tori can be
applied also in more complicated situations. We show that -algebras appear
naturally in Fedosov construction of formal deformation of commutative algebras
of functions and that similar -algebras can be constructed also in the case
when the deformation parameter is not formal.Comment: Extended version of hep-th/991221
General properties of the boundary renormalization group flow for supersymmetric systems in 1+1 dimensions
We consider the general supersymmetric one-dimensional quantum system with
boundary, critical in the bulk but not at the boundary. The renormalization
group flow on the space of boundary conditions is generated by the boundary
beta functions \beta^{a}(\lambda) for the boundary coupling constants
\lambda^{a}. We prove a gradient formula \partial\ln z/\partial\lambda^{a}
=-g_{ab}^{S}\beta^{b} where z(\lambda) is the boundary partition function at
given temperature T=1/\beta, and g_{ab}^{S}(\lambda) is a certain
positive-definite metric on the space of supersymmetric boundary conditions.
The proof depends on canonical ultraviolet behavior at the boundary. Any system
whose short distance behavior is governed by a fixed point satisfies this
requirement. The gradient formula implies that the boundary energy,
-\partial\ln z/\partial\beta = -T\beta^{a}\partial_{a}\ln z, is nonnegative.
Equivalently, the quantity \ln z(\lambda) decreases under the renormalization
group flow.Comment: 21 pages, Late
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