M-theory Flux Research Articles

T-duality and flavor symmetries in Little String Theories

We explore the T-duality web of 6D Heterotic Little String Theories, focusing on flavor algebra reducing deformations. A careful analysis of the full flavor algebra, including Abelian factors, shows that the flavor rank is preserved under T-duality. This suggests a new T-duality invariant in addition to the Coulomb branch dimension and the two-group structure constants. We also engineer Little String Theories with non-simply laced flavor algebras, whose appearance we attribute to certain discrete 3-form fluxes in M-theory. Geometrically, these theories are engineered in F-theory with non-Kähler favorable K3 fibers. This geometric origin leads us to propose that freezing fluxes are preserved across T-duality. Along the way, we discuss various exotic models, including two inequivalent Spin(32)/ℤ2 models that are dual to the same E8 × E8 theory, and a family of self-T-dual models.

Quantum black hole entropy, localization and the stringy exclusion principle

Supersymmetric localization has led to remarkable progress in computing quantum corrections to BPS black hole entropy. The program has been successful especially for computing perturbative corrections to the Bekenstein-Hawking area formula. In this work, we consider non-perturbative corrections related to polar states in the Rademacher expansion, which describes the entropy in the microcanonical ensemble. We propose that these non-perturbative effects can be identified with a new family of saddles in the localization of the quantum entropy path integral. We argue that these saddles, which are euclidean AdS2 × S1 × S2 geometries, arise after turning on singular fluxes in M-theory on a Calabi-Yau. They cease to exist after a certain amount of flux, resulting in a finite number of geometries; the bound on that number is in precise agreement with the stringy exclusion principle. Localization of supergravity on these backgrounds gives rise to a finite tail of Bessel functions in agreement with the Rademacher expansion. As a check of our proposal, we test our results against well known microscopic formulas for one-eighth and one-quarter BPS black holes in mathcal{N}=8 and mathcal{N}=4 string theory respectively, finding agreement. Our method breaks down precisely when mock-modular effects are expected in the entropy of one-quarter BPS dyons and we comment upon this. Furthermore, we mention possible applications of these results, including an exact formula for the entropy of four dimensional mathcal{N}=2 black holes.

Alpha- and Omega-deformations from fluxes in M-theory

We discuss an SL(2,R) family of deformed N=2 four-dimensional gauge theories which we derive from a flux background in M-theory. In addition to the Omega-deformation this family includes a new deformation, which we call the Alpha-deformation, which can be viewed as an S-dual to the Omega-deformation. We study these gauge theories in two ways: by constructing a non-Abelian (but UV-complete) Lagrangian, and by their strong coupling lift to M-theory where their low-energy dynamics can be determined by examining the equation of motion of a single M5-brane wrapped on a Riemann surface.

A second look at gauged supergravities from fluxes in M-theory

We investigate reductions of M-theory beyond twisted tori by allowing the presence of KK6 monopoles (KKO6-planes) compatible with N=4 supersymmetry in four dimensions. The presence of KKO6-planes proves crucial to achieve full moduli stabilisation as they generate new universal moduli powers in the scalar potential. The resulting gauged supergravities turn out to be compatible with a weak G2 holonomy at N=1 as well as at some non-supersymmetric AdS4 vacua. The M-theory flux vacua we present here cannot be obtained from ordinary type IIA orientifold reductions including background fluxes, D6-branes (O6-planes) and/or KK5 (KKO5) sources. However, from a four-dimensional point of view, they still admit a description in terms of so-called non-geometric fluxes. In this sense we provide the M-theory interpretation for such non-geometric type IIA flux vacua.

Type IIA supergravity andM-theory on manifolds withSU(4)structure

We give the general form of supersymmetric backgrounds with two real supercharges of M theory and type IIA supergravity (with nonzero Romans mass in general) of the form ${\mathbb{R}}^{1,d}\ifmmode\times\else\texttimes\fi{}{\mathcal{M}}_{8}$, $d=1,2$, on eight-dimensional manifolds with $SU(4)$ structure. We point out a subtlety in the integrability theorems for low-dimensional supersymmetric compactifications. As a special case we examine Calabi-Yau flux vacua, and we show that unbroken supersymmetry does not in general require the 4-form flux to be (2,2) or primitive. Our results could be used to construct novel higher dimensional analogues of the Klebanov-Strassler geometry. In the case of M-theory large-volume Calabi-Yau flux vacua, our results are in agreement with partial supersymmetry breaking in three-dimensional $\mathcal{N}=2$ supergravity. Alternatively, the conditions for supersymmetry can be expressed in terms of a real ``superpotential'' in accordance with three-dimensional $\mathcal{N}=1$ supergravity. We present explicit examples of M-theory flux vacua on $\mathrm{K}3\ifmmode\times\else\texttimes\fi{}\mathrm{K}3$, which however do not appear to possess $F$-theory duals with four-dimensional Poincar\'e invariance.

S-Track stabilization of heterotic de Sitter vacua

We present a new mechanism, the $S$-Track, to stabilize the volume modulus $S$ in heterotic M-theory flux compactifications along with the orbifold size $T$ besides complex structure and vector bundle moduli stabilization. The key dynamical ingredient which makes the volume modulus stabilization possible, is M5 instantons arising from M5 branes wrapping the whole Calabi-Yau slice. These are natural in heterotic M theory where the warping shrinks the Calabi-Yau volume along ${\mathbf{S}}^{1}/{\mathbf{Z}}_{2}$. Combined with $H$ flux, open M2 instantons, and hidden sector gaugino condensation it leads to a superpotential $W$ which stabilizes $S$ similar to a racetrack but without the need for multi-gaugino condensation. Moreover, $W$ contains two competing nonperturbative effects which stabilize $T$. We analyze the potential and superpotentials to show that it leads to heterotic de Sitter vacua with broken supersymmetry through nonvanishing F terms.

Features of de Sitter vacua in M-theory

We compute the masses of all moduli in the unstable deSitter vacua arising in the toy model of cosmological M-theory flux compactifications on the G2 holonomy manifolds of [1]. The slow-roll parameters in the tachyonic directions are shown to be too large to be useful for conventional models of inflation. However, it appears that we can find fast roll regimes which could, under certain conditions, account for the current dark energy driven accelerated expansion of the universe.

Fluxes in M-theory on 7-manifolds: G-structures and superpotential

We consider compactifications of M-theory on 7-manifolds in the presence of 4-form fluxes, which leave at least four supercharges unbroken. We focus especially on the case, where the fluxes on the 7-manifold are consistent with SU(3) singlet spinors and hence appear as specific SU(3) structures. We derive the constraints on the fluxes imposed by supersymmetry and determine the flux components that fix the resulting 4-dimensional cosmological constant (or superpotential).