In a previous paper a method was proposed to find exact analytic solutions of open string field theory describing lower dimensional lumps, by incorporating in string field theory an exact renormalization group flow generated by a relevant operator in a worldsheet CFT. In this paper we compute the energy of one such solution, which is expected to represent a D24 brane. We show, both numerically and analytically, that its value corresponds to the theoretically expected one.Comment: 45 pages, former section 2 suppressed, Appendix D added, comments and references added, typos corrected. Erratum adde
We propose a remarkably simple solution of cubic open string field theory which describes inhomogeneous tachyon condensation. The solution is in one-to-one correspondence with the IR fixed point of the RG-flow generated in the two-dimensional worldsheet theory by integrating a relevant operator with mild enough OPE on the boundary. It is shown how the closed string overlap correctly captures the shift in the closed string one point function between the UV and the IR limits of the flow. Examples of lumps in non-compact and compact transverse directions are given.
We test the holographic relation between the vacuum expectation values of gauge invariant operators in N = 6 U k (N ) × U −k (N ) mass-deformed ABJM theory and the LLM geometries with Z k orbifold in 11-dimensional supergravity. To do so, we apply the Kaluza-Klein reduction to construct a 4-dimensional gravity theory and implement the holographic renormalization procedure. We obtain an exact holographic relation for the vacuum expectation values of the chiral primary operator with conformal dimension = 1, which is given by, for large N and k = 1. Here the factor f ( ) is independent of N . Our results involve an infinite number of exact dual relations for all possible supersymmetric Higgs vacua and so provide a non-trivial test of gauge/gravity duality away from the conformal fixed point. We extend our results to the case of k = 1 for LLM geometries represented by rectangularshaped Young diagrams. We also discuss the exact mapping of the gauge/gravity at finite N for classical supersymmetric vacuum solutions in field theory side and corresponding classical solutions in gravity side.
We construct the interaction terms between the world-volume fields of multiple M2branes and the 3-and 6-form fields in the context of ABJM theory with U(N )×U(N ) gauge symmetry. A consistency check is made in the simplest case of a single M2-brane i.e., our construction matches the known effective action of M2-brane coupled to antisymmetric 3-form field. We show that when dimensionally reduced, our couplings coincide with the effective action of D2-branes coupled to R-R 3-and 5-form fields in type IIA string theory.We also comment on the relation between a coupling with a specific 6-form field configuration and the supersymmetry preserving mass deformation in ABJM theory.Recently, the Lagrangian descriptions of multiple M2-branes were found in the low energy limit, which are the Bagger-Lambert-Gustavsson(BLG) theory [1, 2] and the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory [3]. The BLG theory, which is equivalent to the ABJM theory with SU(2)×SU(2) gauge group [4], has N = 8 supersymmetry and it is an effective theory of two M2-branes. The ABJM theory with U(N)×U(N) gauge group has N = 6 supersymmetry and it describes the dynamics of N parallel M2-branes sitting at the singularity of a space with Z k orbifold, where k appears as the Chern-Simons level in the theory.Low energy dynamics of D-branes is also depicted by supersymmetric gauge theories, i.e., it is the Dirac-Born-Infeld(DBI) action or the super Yang-Mills theory to the leading order in α ′expansion. In addition, D-branes can couple to the bulk supergravity fields. The bosonic bulk fields include R-R form fields, which couple to the D-branes through Wess-Zumino(WZ)-type action [5,6,7]. In the case of single Dp-brane, the WZ-type coupling is only to the R-R form fields of rank p + 1 or less. For multiple Dp-branes the action can include the couplings to all kinds of R-R form fields [7].
This paper is primarily devoted to the ghost wedge states in string field theory formulated with the oscillator formalism. Our aim is to prove, using such formalism, that the wedge states can be expressed as |n = exp 2−n 2 L 0 + L † 0 |0 , separately in the matter and ghost sector. This relation is crucial for instance in the proof of Schnabl's solution. We start from the exponentials in the rhs and wish to prove that they take precisely the form of wedge states. As a guideline we first re-demonstrate this relation for the matter part. Then we turn to the ghosts. On the way we face the problem of 'diagonalizing' infinite rectangular matrices. We manage to give a meaning to such an operation and to prove that the eigenvalues we obtain satisfy the recursion relations of the wedge states.
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