Anomaly free effective action for the elementary M5-brane

We construct an effective action describing an elementary M5-brane interacting with dynamical eleven-dimensional supergravity, which is free from gravitational anomalies. The current associated to the elementary brane is taken as a distribution valued δ-function on the support of the 5-brane itself. Crucial ingredients of the construction are the consistent inclusion of the dynamics of the chiral two-form on the 5-brane, and the use of an invariant Chern-kernel allowing to introduce a D=11 three-form potential which is well-defined on the worldvolume of the 5-brane.     

Algebraic form of the M3-brane action

We reformulate the bosonic action of an unstable M3-brane to manifest its algebraic representation. It is seen that in contrast to string and M2-brane actions, which are respectively represented only in terms of two- and three-dimensional Lie algebras, the algebraic form of the M3-brane action is a combination of four-, three-, and two-dimensional Lie algebras. Corresponding brackets appear as mixtures of the tachyon field, space-time coordinates X, the two-form field \(\hat \omega ^{(2)}\) , and the Born-Infeld one-form \(\hat b_\mu\) .     

Exact holography of the mass-deformed M2-brane theory

We test the holographic relation between the vacuum expectation values of gauge invariant operators in \({\mathcal {N}} = 6\) U\(_k(N)\times \mathrm{U}_{-k}(N)\) mass-deformed ABJM theory and the LLM geometries with \({\mathbb {Z}}_k\) 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 \(\Delta = 1\), which is given by \(\langle {\mathcal {O}}^{(\Delta =1)}\rangle = N^{\frac{3}{2}} \, f_{(\Delta =1)}\), for large N and \(k=1\). Here the factor \(f_{(\Delta )}\) 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 \(k\ne 1\) for LLM geometries represented by rectangular-shaped 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.     

Truncations of the D9-brane action and type-I strings

The low-energy effective action of type-I superstring theory in ten dimensions is obtained performing a truncation of type-IIB supergravity in a background where D9-branes are present. The open sector corresponds to the first order in the low-energy expansion of the D9-brane action in a type-I background. In hep-th/9901055 it was shown that there are two ways of performing a type-I truncation of the D9-brane action, and the resulting truncated action was obtained in a flat background. We extend this result to a generic type-I background, and argue that the two different truncations are in correspondence with the open sector of the low-energy effective action of the two different consistent ten-dimensional type-I string theories, namely the SO(32) superstring and the USp(32) non-supersymmetric string.     

Holography of massive M2-brane theory: non-linear extension

We investigate the gauge/gravity duality between the \(\mathcal{N} = 6\) mass-deformed ABJM theory with \(\hbox {U}_k(N)\times \hbox {U}_{-k}(N)\) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1)\(\times \)SO(4)/\({\mathbb {Z}}_k\) \(\times \)SO(4)/\({\mathbb {Z}}_k\) isometry, in terms of a KK holography, which involves quadratic order field redefinitions. We establish the quadratic order KK mappings for various gauge invariant fields in order to obtain the canonical 4-dimensional gravity equations of motion and to reduce the LLM solutions to an asymptotically AdS\(_4\) gravity solutions. The non-linearity of the KK maps indicates that we can observe the true purpose of the non-linear KK holography of the LLM solutions. We read the vacuum expectation value of conformal dimension two operator from the asymptotically AdS\(_4\) gravity solutions. For the LLM solutions which are represented by square-shaped Young diagrams, we compare the vacuum expectation value obtained from the holographic procedure with the result obtained from the field theory, which is given by \(\langle \mathcal{O}^{(\Delta =2)}\rangle =\sqrt{k}N^{\frac{3}{2}}f_{(\Delta =2)}+\mathcal{O}(N)\), where \(f_{\Delta }\) is independent of N. Based on this result, we examine the gauge/gravity duality in the large N limit and finite k. We also show that the vacuum expectation values of the massive KK graviton modes are vanishing as expected by the supersymmetry.     

A dual formulation of supergravity-matter theories

Generating supersymmetric AdS solutions in non-minimal supergravity in four dimensions is notoriously difficult. Indeed, it is a longstanding lore that such solutions exist only for old minimal supergravity. In this paper, we construct a dual formulation for general N=1 supergravity-matter systems that avoids the problem. In the case of pure supergravity without a cosmological constant, it coincides with the usual non-minimal (n=−1) supergravity, but in the presence of matter (or a cosmological constant) our formulation differs considerably. We also elaborate upon the framework of conformal superspace and the compensator method as applied to our theory. In particular, we show that one can encode the details of the Kähler potential and superpotential entirely within the geometry of superspace so that the general sigma-model action is encoded in a single compact term: the supervolume. Finally, we discuss the issue of supercurrents and propose a general form for the supercurrent in AdS.     

Manifestly dual formulation of the Ramond-model

The interacting-string formalism is extended to the Neveu-Schwarz and Ramond models. The duality properties of the latter model are more transparent than in the older formulation, and ghost-free amplitudes with an arbitrary number of external fermions can be calculated.     

Towards Abelian-like formulation of the dual gluodynamics

We consider gluodynamics in case when both color and magnetic charges are present. We discuss first short distance physics, where only the fundamental |Q_m|=1 monopoles introduced via the 't Hooft loop can be considered consistently. We show that at short distances the external monopoles interact as pure Abelian objects. This result can be reproduced by a Zwanziger-type Lagrangian with an Abelian dual gluon and ordinary gluons in an adjoint representation. We introduce also an effective dual gluodynamics which might be a valid approximation at distances where the monopoles |Q_m|=2 can be considered as point-like as well. Assuming the monopole condensation we arrive at a model which is reminiscent in some respect of the Abelian Higgs model but, unlike the latter leaves space for the Casimir scaling.     

Fuzzball solutions for black holes and D1-brane-D5-brane microstates

We revisit the relation between fuzzball solutions and D1-brane-D5-brane microstates. A consequence of the fact that the R ground states (in the usual basis) are eigenstates of the R charge is that only neutral operators can have nonvanishing expectation values on these states. We compute the holographic 1-point functions of the fuzzball solutions and find that charged chiral primaries have nonzero expectation values, except when the curve characterizing the solution is circular. The nonzero vacuum expectation values reflect the fact that a generic curve breaks R symmetry completely. This implies that fuzzball solutions (excepting circular ones) can only correspond to superpositions of R states and we give a proposal for the superposition corresponding to a given curve. We also address the question of what would be the geometric dual of a given R ground state.     

Unambiguous field-strength formulation and dual potentials for gauge theories

Using completely fixed axial-like gauges, I construct the unique inversion A(F) for the potential A in terms of the field strength F. A change of variable to F results in an unambiguous field-strength formulation for any gauge theory; F is constrained to satisfy the Bianchi identities $\text{?}\text{F}\text{～}\text{? eA(F)}\text{F}\text{～}\text{= 0}$. Dual potentials $\text{A}\text{～}$ may also be introduced as functional Fourier conjugate to the Bianchi forms. For quantum electrodynamics in four dimensions, duality $\text{[F ?}\text{F}\text{～}$, $\text{A ?}\text{F}\text{～}$ is a perfect symmetry. Residuals of this symmetry persist in all theories however; e.g., $\text{F}\text{～}$ is always canonically conjugate to the magnetic fields.     

Hamilton-Jacobi formulation of the Harada gauged Floreanini-Jackiw action

We study the front-form Harada gauged Floreanini-Jackiw action and its BRST-anti-BRST symmetry within Hamilton-Jacobi formalism. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. This paper is partially supported by the Scientific and Technical Research Council of Turkey.     

Frame-like action and unfolded formulation for massive higher-spin fields

Unfolded equations of motion for symmetric massive bosonic fields of any spin in Minkowski and (A)dS$(A)\mathit{dS}$ spaces are presented. Manifestly gauge invariant action for a spin s?2$s?2$ massive field in any dimension is constructed in terms of gauge invariant curvatures.