Edge Critical Behaviour of the 2-Dimensional Tri-critical Ising Model

Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling constant. A boundary tri-critical point separates phases where the spins on the boundary are ordered or disordered. In the latter range of coupling constant, there is a non-zero critical field where the magnetization is singular. In the former range, as the temperature is lowered, the boundary undergoes a first order transition while the bulk simultaneously undergoes a second order transition.Comment: 6 pages, RevTex, 3 postscript figure

D-branes in the WZW model

It is stated in the literature that D-branes in the WZW-model associated with the gluing condition J = - \bar{J} along the boundary correspond to branes filling out the whole group volume. We show instead that the end-points of open strings are rather bound to stay on `integer' conjugacy classes. In the case of SU(2) level k WZW model we obtain k-1 two dimensional Euclidean D-branes and two D particles sitting at the points e and -e.Comment: 2 pages, LaTe

DBI analysis of generalised permutation branes

We investigate D-branes on the product GxG of two group manifolds described as Wess-Zumino-Novikov-Witten models. When the levels of the two groups coincide, it is well known that there exist permutation D-branes which are twisted by the automorphism exchanging the two factors. When the levels are different, the D-brane charge group demands that there should be generalisations of these permutation D-branes, and a geometric construction for them was proposed in hep-th/0509153. We give further evidence for this proposal by showing that the generalised permutation D-branes satisfy the Dirac-Born-Infeld equations of motion for arbitrary compact, simply connected and simple Lie groups G.Comment: 19 pages, computation in section 3.5.1 corrected, conclusions unchange

Orientifolds of type IIA strings on Calabi-Yau manifolds

We identify type IIA orientifolds that are dual to M-theory compactifications on manifolds with G_2-holonomy. We then discuss the construction of crosscap states in Gepner models. (Based on a talk presented by S.G. at PASCOS 2003 held at the Tata Institute of Fundamental Research, Mumbai during Jan. 3-8, 2003.)Comment: 3 pages, RevTeX, PASCOS '03 tal

Gravitino condensation in fivebrane backgrounds

We calculate the tension of the D3-brane in the fivebrane background which is described by the exactly solvable SU(2)_k x U(1) world-sheet conformal field theory with large Kac-Moody level k. The D3-brane tension is extracted from the amplitude of one closed string exchange between two parallel D3-branes, and the amplitude is calculated by utilizing the open-closed string duality. The tension of the D3-brane in the background does not coincide with the one in the flat space-time even in the flat space-time limit: k -> infinity. The finite curvature effect should vanish in the flat space-time limit and only the topological effect can remain. Therefore, the deviation indicates the condensation of gravitino and/or dilatino which has been expected in the fivebrane background as a gravitational instanton.Comment: 16 pages, 1 figur

Twisted boundary states in c=1 coset conformal field theories

We study the mutual consistency of twisted boundary conditions in the coset conformal field theory G/H. We calculate the overlap of the twisted boundary states of G/H with the untwisted ones, and show that the twisted boundary states are consistently defined in the diagonal modular invariant. The overlap of the twisted boundary states is expressed by the branching functions of a twisted affine Lie algebra. As a check of our argument, we study the diagonal coset theory so(2n)_1 \oplus so(2n)_1/so(2n)_2, which is equivalent with the orbifold S^1/\Z_2. We construct the boundary states twisted by the automorphisms of the unextended Dynkin diagram of so(2n), and show their mutual consistency by identifying their counterpart in the orbifold. For the triality of so(8), the twisted states of the coset theory correspond to neither the Neumann nor the Dirichlet boundary states of the orbifold and yield the conformal boundary states that preserve only the Virasoro algebra.Comment: 44 pages, 1 figure; (v2) minor change in section 2.3, references adde

The Landau-Ginzburg to Calabi-Yau Dictionary for D-Branes

Based on work by Orlov, we give a precise recipe for mapping between B-type D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the corresponding large-radius Calabi-Yau manifold. The D-branes in Landau-Ginzburg theories correspond to matrix factorizations and the D-branes on the Calabi-Yau manifolds are objects in the derived category. We give several examples including branes on quotient singularities associated to weighted projective spaces. We are able to confirm several conjectures and statements in the literature.Comment: 24 pages, refs added + minor correctio

Generalised permutation branes

We propose a new class of non-factorising D-branes in the product group GxG where the fluxes and metrics on the two factors do not necessarily coincide. They generalise the maximally symmetric permutation branes which are known to exist when the fluxes agree, but break the symmetry down to the diagonal current algebra in the generic case. Evidence for the existence of these branes comes from a Lagrangian description for the open string world-sheet and from effective Dirac-Born-Infeld theory. We state the geometry, gauge fields and, in the case of SU(2)xSU(2), tensions and partial results on the open string spectrum. In the latter case the generalised permutation branes provide a natural and complete explanation for the charges predicted by K-theory including their torsion.Comment: 33 pages, 6 figures, v2: Extended discussion of K-theory interpretation of our branes for products of higher rank groups in the conclusions; v3: Correction of formula (35) and adjustment of the discussion below equation (45) (no change of result). Footnote 9 points out a previously unnoticed subtlety and provides a reference to a more detailed discussio

Particle models from orientifolds at Gepner-orbifold points

We consider configurations of stacks of orientifold planes and D-branes wrapped on a non trivial internal space of the structure {(Gepner model)^{c=3n} x T^{2(3-n)}}/Z_N, for n=1,2,3. By performing simple moddings by discrete symmetries of Gepner models at orienti fold points, consistent with a Z_N orbifold action, we show that projection on D-brane configurations can be achieved, generically leading to chiral gauge theories. Either supersymmetric or non-supersymmetric (tachyon free) models can be obtained. We illustrate the procedure through some explicit examples.Comment: 36 pages, no figures Corrected sign of eq. 6.26 references added, minor correction

Tensor Product and Permutation Branes on the Torus

We consider B-type D-branes in the Gepner model consisting of two minimal models at k=2. This Gepner model is mirror to a torus theory. We establish the dictionary identifying the B-type D-branes of the Gepner model with A-type Neumann and Dirichlet branes on the torus.Comment: 26 page