RR Fluxes Research Articles

Compactification with flux on K3 and tori

We study compactifications of Type IIB string theory on a K3 \times T^2/Z_2 orientifold in the presence of RR and NS flux. We find the most general supersymmetry preserving, Poincare invariant, vacua in this model. All the complex structure moduli and some of the Kahler moduli are stabilised in these vacua. We obtain in an explicit fashion the restrictions imposed by supersymmetry on the flux, and the values of the fixed moduli. Some T-duals and Heterotic duals are also discussed, these are non-Calabi-Yau spaces. A superpotential is constructed describing these duals.

Wrapped branes with fluxes in 8d gauged supergravity

We study the gravity dual of several wrapped D-brane configurations in presence of 4-form RR fluxes partially piercing the unwrapped directions. We present a systematic approach to obtain these solutions from those without fluxes. We use D=8 gauged supergravity as a starting point to build up these solutions. The configurations include (smeared) M2-branes at the tip of a G_2 cone on S^3 x S^3, D2-D6 branes with the latter wrapping a special Lagrangian 3-cycle of the complex deformed conifold and an holomorphic sphere in its cotangent bundle T^*S^2, D3-branes at the tip of the generalized resolved conifold, and others obtained by means of T duality and KK reduction. We elaborate on the corresponding N=1 and N=2 field theories in 2+1 dimensions.

Holography with Ramond-Ramond fluxes

Starting from the non-linear sigma model of the IIB string in the light-cone gauge, we analyze the role of RR fluxes in Holography. We find that the worldsheet theory of states with only left or right moving modes does not see the presence of RR fields threading a geometry. We use this significant simplification to compute part of the strong coupling spectrum of the two dimensional NCOS theory. We also reproduce the action of a closed string in a PP-wave background using this general formalism; and we argue for various strategies to find new systems where the closed string theory may be exactly solvable.

Thermal amplitudes in DLCQ superstrings on pp-waves

We calculate the thermal partition function of DLCQ superstring on the maximally supersymmetric pp-wave background, which is realized as the Penrose limit of orbifolded AdS 5× S 5 and known to be dual to the N=2 “large” quiver gauge theory as shown by Mukhi, Rangamani and Verlinde, . Making use of the path-integral technique, we derive the manifestly modular invariant expression and show the equivalence with the free energy of second quantized free superstring on this background. The “virtual strings” wound around the temporal circle play essential roles for realizing the modular invariance and for a simple analysis on the Hagedorn temperature. We also calculate the thermal one-loop amplitudes of open strings under the various backgrounds of the supersymmetric time-like and Euclidean D-branes, and confirm the existence of correct open–closed string duality. Furthermore, we extend these thermodynamical analysis to the 6-dimensional DLCQ pp-waves with general RR and NSNS flux. These superstring vacua are similarly derived from the supersymmetric (half SUSY) and non-supersymmetric orbifolds of AdS 3× S 3× M 4 ( M 4= T 4 or K3) by the appropriate Penrose limits, giving rise to the SUSY enhancement as in the case of orbifolded AdS 5× S 5.

Fluxes and branes in type II vacua and M-theory geometry with G2 and spin(7) holonomy

We discuss fluxes of RR and NSNS background fields in type II string compactifications on non-compact Calabi–Yau threefolds together with their dual brane description which involves bound states of branes. Simultaneously turning on RR and NSNS 2-form fluxes in an 1/2 supersymmetric way can be geometrically described in M-theory by a SL(2, Z) family of metrics of G 2 holonomy. On the other hand, if the flux configuration only preserves 1/4 of supersymmetries, we postulate the existence of a new eight-dimensional manifold with spin(7) holonomy, which does not seem to fit into the classes of known examples. The latter situation is dual to a 1/4 supersymmetric web of branes on the deformed conifold. In addition to the 2-form fluxes, we also present some considerations on type IIA NSNS 4-form and 6-form fluxes.

Type II theories compactified on Calabi–Yau threefolds in the presence of background fluxes

Compactifications of type II theories on Calabi–Yau threefolds including electric and magnetic background fluxes are discussed. We derive the bosonic part of the four-dimensional low energy effective action and show that it is a non-canonical N=2 supergravity which includes a massive two-form. The symplectic invariance of the theory is maintained as long as the flux parameters transform as a symplectic vector and a massive two-form which couples to both electric and magnetic field strengths is present. The mirror symmetry between type IIA and type IIB compactified on mirror manifolds is shown to hold for RR fluxes at the level of the effective action. We also compactify type IIA in the presence of NS three-form flux but the mirror symmetry in this case remains unclear.

G2 holonomy spaces from invariant three-forms

We construct several new G 2 holonomy metrics that play an important role in recent studies of geometrical transitions in compactifications of M-theory to four dimensions. In type IIA string theory these metrics correspond to D6-branes wrapped on the three-cycle of the deformed conifold and the resolved conifold with two-form RR flux on the blown-up two-sphere, which are related by a conifold transition. We also study a G 2 metric that is related in type IIA to the line bundle over S 2× S 2 with RR two-form flux. Our approach exploits systematically the definition of torsion-free G 2 structures in terms of three-forms which are closed and co-closed. Besides being an elegant formalism this turns out to be a practical tool to construct G 2 holonomy metrics.

Matrix dynamics of fuzzy spheres

We study the dynamics of fuzzy two-spheres in a matrix model which represents string theory in the presence of RR flux. We analyze the stability of known static solutions of such a theory which contain commuting matrices and SU(2) representations. We find that irreducible as well as reducible representations are stable. Since the latter are of higher energy, this stability poses a puzzle. We resolve this puzzle by noting that reducible representations have marginal directions corresponding to non-spherical deformations. We obtain new static solutions by turning on these marginal deformations. These solutions now have instability or tachyonic directions. We discuss condensation of these tachyons which correspond to classical trajectories interpolating from multiple, small fuzzy spheres to a single, large sphere. We briefly discuss spatially independent configurations of a D3/D5 system described by the same matrix model which now possesses a supergravity dual.

Gravitational couplings of orientifold planes

We reanalyse the gravitational couplings of the perturbative orientifold planes $Op^-$, $Op^+$ (and D-branes). We first compute their $D_{-1}$ instantonic corrections for $p=3$. Then, by using U-dualities, we obtain the Wess-Zumino terms of orientifolds with RR flux for $p \leq 5$. The expressions for the effective actions can be partially checked via M-theory. We point out a previous oversimplification and we show in fact that the difficulty still stands in the way of the full computation of 7 Brane instanton corrections.

Penrose limits of RG fixed points and PP-waves with background fluxes

We consider a family of pp-wave solutions of IIB supergravity. This family has a non-trivial, constant 5-form flux, and non-trivial, (light-cone) time-dependent RR and NS-NS 3-form fluxes. The solutions have either 16 or 20 supersymmetries depending upon the time dependence. One member of this family of solutions is the Penrose limit of the solution obtained by Pilch and Warner as the dual of a Leigh-Strassler fixed point. The family of solutions also provides indirect evidence in support of a recent conjecture concerning a large N duality group that acts on RG flows of N=2 supersymmetric, quiver gauge theories.

Type IIB supergravity compactified on a Calabi-Yau manifold with H-fluxes

We discuss the compactification of type IIB supergravity on a Calabi-Yau manifold in the presence of both RR and NS fluxes for the three-form fields. We obtain the classical potential both by direct compactification and by using the techniques of N=2 gauged supergravity in four-dimensions. We briefly discuss the properties of such potential and compare the result with previous derivations.

Dielectric D0-branes in near-horizon D-brane backgrounds and D-strings under electric RR fluxes

Using the nonabelian Dirac–Born–Infeld action with the Wess–Zumino term that is constructed in consistent with T duality we examine the Myers dielectric effect for multiple D0-branes in the near-horizon geometry of D4-branes. The effect in the curved spacetime is also confirmed by the dual formulation based on the abelian Dirac–Born–Infeld action of a D2-brane. Putting a system of multiple D-strings in the external electric RR five-form flux, we construct a noncommutative funnel-like solution where the D-strings expand into a spherical D3-brane. We discuss the external field dependence of the funnel-like or wormhole solution.

Orientifolds, RR torsion, and K-theory

We analyze the role of RR fluxes in orientifold backgrounds from the point of view of K-theory, and demonstrate some physical implications of describing these fluxes in K-theory rather than cohomology. In particular, we show that certain fractional shifts in RR charge quantization due to discrete RR fluxes are naturally explained in K-theory. We also show that some orientifold backgrounds, which are considered distinct in the cohomology classification, become equivalent in the K-theory description, while others become unphysical.

Return of the torsion D-branes

We study D-branes on Calabi-Yau manifolds, carrying charges which are torsion elements of the K-theory. Interesting physics ensues when we follow these branes into nongeometrical phases of the compactification. On the level of K-theory, we determine the monodromies of the group of charges as we circle singular loci in the closed string moduli space. Going beyond K-theory, we discuss the stability of torsion D-branes as a function of the K\ahler moduli. When the fundamental group of the Calabi-Yau is nonabelian, we find evidence for new threshold bound states of BPS branes. In a two-parameter example, we compare our results with computations in the Gepner model. Our study of the torsion D-branes in the compactification of [FHSV] sheds light on the physics of that model. In particular, we develop a proposal for the group of allowed D-brane charges in the presence of discrete RR fluxes.

M-theory, orientifolds and G-flux

We study the properties of M and F theory compactifications to three and four dimensions with background fluxes. We provide a simple construction of supersymmetric vacua, including some with orientifold descriptions. These vacua, which have warp factors, typically have fewer moduli than conventional Calabi-Yau compactifications. The mechanism for anomaly cancellation in the orientifold models involves background RR and NS fluxes. We consider in detail an orientifold of $K3\times T^2$ with background fluxes. After a combination of T and S-dualities, this type IIB orientifold is mapped to a compactification of the SO(32) heterotic string on a non-Kahler space with torsion.