Melvin Background Research Articles

D-branes in Melvin background

In this paper we discuss D-branes in the Melvin background and its supersymmetric generalizations. In particular we determine the D-brane spectra in these backgrounds by constructing their boundary states explicitly, where some of the D-branes are supersymmetric. The results sensitively depend on whether the value of magnetic flux in the Melvin background is rational or irrational. For the rational case the D-branes are regarded as the generalizations of fractional D-branes in abelian orbifolds n/N of type-II or type-0 string theory. For the irrational case we found a very limited spectrum. Since the background includes the non-trivial H-flux, the D-branes will provide interesting examples from the viewpoint of the non-commutative geometry.

Fluxbranes fromp-branes

It is shown how magnetic fluxbrane, Fp-brane, solutions are related to electric black p-branes by analytic continuation. Viewing the transverse space of branes as a warped cone, one finds that the cone base of the p-brane becomes the world-volume of the $F(\mathrm{D}\ensuremath{-}p\ensuremath{-}3)$-brane and the world volume of the p-brane becomes the cone base of the $F(\mathrm{D}\ensuremath{-}p\ensuremath{-}3)$-brane. An explicit example of the correspondence is given for a 2-brane and F6-brane of $11\mathrm{D}$ supergravity.

Closed string tachyons in non-supersymmetric heterotic theories

We calculate partition functions for supersymmetric heterotic theories on Melvin background with Wilson line. These functions coincide with partition functions for some of non-supersymmetric heterotic theories in appropriate limits. This suggests that non-supersymmetric heterotic theories are equivalent to supersymmetric theories on supersymmetry-breaking backgrounds, just as in the case of recently conjectured IIA-0A duality.

The Kaluza Klein Melvin solution in M-theory

We study some aspects of the Kaluza-Klein Melvin solution in M-theory. The associated magnetic field has a maximal critical value $B=\pm 1/R$ where $R$ is the radius of the compactification circle. It is argued that the Melvin background of type IIA with magnetic field $B$ and of type 0A with magnetic field $B'=B-1/R$ are equivalent. Evidence for this conjecture is provided using a further circle compactification and a `9-11' flip. We show that partition functions of nine-dimensional type IIA strings and of a $(-1)^F\sigma_{1/2}$ type IIA orbifold both with NS-NS Melvin fluxtubes are related by such shift of the magnetic field. Then the instabilities of both IIA and 0A Melvin solutions are analyzed. For each theory there is an instanton associated to the decay of spacetime. In the IIA case the decay mode is associated to the nucleation of $D6/D\bar{6}$-brane pairs, while in the 0A case spacetime decays through Witten's bubble production.

Magnetic flux tube models in superstring theory

Superstring models describing curved 4-dimensional magnetic flux tube backgrounds are exactly solvable in terms of free fields. We first consider the simplest model of this type (corresponding to a ‘Kaluza-Klein’ a = √3 Melvin background). Its 2d action has a flat but topologically non-trivial 10-dimensional target space (there is a mixing of the angular coordinate of the 2-plane with an internal compact coordinate). We demonstrate that this theory has broken supersymmetry but is perturbatively stable if the radius R of the internal coordinate is larger than R 0 = √2 α′. In the Green-Schwarz formulation the supersymmetry breaking is a consequence of the presence of a flat but non-trivial connection in the fermionic terms in the action. For R < R 0 and the magnetic field strength parameter q > R/2 α′, instabilities appear corresponding to tachyonic winding states. The torus partition function Z( q, R) is finite for R > R 0 and vanishes for qR = 2 n ( n integer). At the special points qR = 2 n (2 n + 1) the model is equivalent to the free superstring theory compactified on a circle with periodic (antiperiodic) boundary conditions for space-time fermions. Analogous results are obtained for a more general class of static magnetic flux tube geometries including the a = 1 Melvin model.

Melvin solution in string theory

We identify string theory counterpart of the dilatonic Melvin D = 4 background describing a “magnetic flux tube” in low-energy field theory limit. The corresponding D = 5 bosonic string model containing extra compact Kaluza-Klein dimension is a direct product of the D = 2 Minkowski space and a D = 3 conformal σ-model. The latter is a singular limit of the [SL(2,R) × R] R gauged WZW theory. This implies, in particular, that the dilatonic Melvin background is an exact string solution to all orders in α 1. Moreover, the D = 3 model is formally related by an abelian duality to a flat space of non-trivial topology. The conformal field theory for the Melvin solution is exactly solvable (and for special values of magnetic field parameter is equivalent to CFT for a Zn orbifold of 2-plane times a circle) and should exhibit tachyonic instabilities.

Pair creation of dilaton black holes.

We consider dilaton gravity theories in four spacetime dimensions parametrized by a constant a, which controls the dilaton coupling, and construct new exact solutions. We first generalize the C metric of Einstein-Maxwell theory (a=0) to solutions corresponding to oppositely charged dilaton black holes undergoing uniform acceleration for general a. We next develop a solution-generating technique which allows us to ``embed'' the dilaton C metrics in magnetic dilaton Melvin backgrounds, thus generalizing the Ernst metric of Einstein-Maxwell theory. By adjusting the parameters appropriately, it is possible to eliminate the nodal singularities of the dilaton C metrics. For a1 (but not for a\ensuremath{\ge}1), it is possible to further restrict the parameters so that the dilaton Ernst solutions have a smooth Euclidean section with topology ${\mathit{S}}^{2}$\ifmmode\times\else\texttimes\fi{}${\mathit{S}}^{2}$-{pt}, corresponding to instantons describing the pair production of dilaton black holes in a magnetic field. A different restriction on the parameters leads to smooth instantons for all values of a with topology ${\mathit{S}}^{2}$\ifmmode\times\else\texttimes\fi{}${\mathit{openR}}^{2}$.

Meson Lagrangians in a superconductor quark model: M. K. Volkov. Joint Institute for Nuclear Research, Dubna, U.S.S.R.

We identify string theory counterpart of the dilatonic Melvin D = 4 background describing a “magnetic flux tube” in low-energy field theory limit. The corresponding D = 5 bosonic string model containing extra compact Kaluza-Klein dimension is a direct product of the D = 2 Minkowski space and a D = 3 conformal σ-model. The latter is a singular limit of the [SL(2,R) × R]R gauged WZW theory. This implies, in particular, that the dilatonic Melvin background is an exact string solution to all orders in α1. Moreover, the D = 3 model is formally related by an abelian duality to a flat space of non-trivial topology. The conformal field theory for the Melvin solution is exactly solvable (and for special values of magnetic field parameter is equivalent to CFT for a Zn orbifold of 2-plane times a circle) and should exhibit tachyonic instabilities.