We discuss the properties of massive type IIA flux compactifications. In particular, we investigate in which case one can obtain dS vacua at large volume and small coupling. We support a general discussion of scaling symmetries with the analysis of a concrete example. We find that the large volume and weak coupling limit requires a large number of O6-planes. Since these are bound for any given compactification space one cannot get arbitrarily good control over α and string loop corrections. arXiv:1811.07880v2 [hep-th]

From the analysis of the near horizon geometry and supersymmetry algebra it has been argued that all the microstates of single centered BPS black holes with four unbroken supersymmetries carry zero angular momentum in the region of the moduli space where the black hole description is valid. A stronger form of the conjecture would be that the result holds for any sufficiently generic point in the moduli space. In this paper we set out to test this conjecture for a class of black hole microstates in type II string theory on T 6 , represented by four stacks of D-branes wrapped on various cycles of T 6 . For this system the above conjecture translates to the statement that the moduli space of classical vacua must be a collection of points. Explicit analysis of systems carrying a low number of D-branes supports this conjecture.

Exact results for the BPS index are known for a class of BPS dyons in type II string theory compactified on a six dimensional torus. In this paper we set up the problem of counting the same BPS states in a duality frame in which the states carry only Ramond-Ramond charges. We explicitly count the number of states carrying the lowest possible charges and find agreement with the result obtained in other duality frames. Furthermore, we find that after factoring out the supermultiplet structure, each of these states carry zero angular momentum. This is in agreement with the prediction obtained from a representation of these states as supersymmetric black holes.

Towards the goal of extracting the continuum properties, we have studied the Topological Charge Density Correlator (TCDC) and the Inverse Participation Ratio (IPR) for the topological charge density (q(x)) in SU(3) Lattice Yang-Mills theory for relatively small lattice spacings including some smaller than those explored before. With the help of recently proposed open boundary condition, it is possible to compute observables at a smaller lattice spacing since trapping problem is absent. On the other hand, the reference energy scale provided by Wilson flow allows us to study their scaling behavior in contrast to previously proposed smearing techniques. The behavior of TCDC for different lattice spacings at a fixed HYP smearing level shows apparent scaling violations. In contrast, at a particular Wilson flow time t for all the lattice spacings investigated (except the largest one), the TCDC data show universal behavior within our statistical uncertainties. The continuum properties of TCDC are studied by investigating the small flow time behavior. We have also extracted the pseudoscalar glueball mass from TCDC, which appears to be insensitive to the lattice spacings (0.0345 fm ≤ a ≤ 0.0667 fm) and agrees with the value extracted using anisotropic lattices, within statistical errors. Further, we have studied the localization property of q(x) through IPR whose continuum behavior can be probed through the small values of Wilson flow time and observed the decrease of IPR with decreasing Wilson flow time. A detailed study of q(x) under Wilson flow time revealed that as Wilson flow time decreases, the proximity of the regions of positive and negative charge densities of large magnitudes increases, and the charge density appears to be more delocalized resulting in the observed behavior of IPR.

We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.

We compute logarithmic corrections to the twisted index B g 6 in fourdimensional N = 4 and N = 8 string theories using the framework of the Quantum Entropy Function. We find that these vanish, matching perfectly with the large-charge expansion of the corresponding microscopic expressions.

A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for the range of lattice scales explored in the range 3 GeV ≤ 1 a ≤ 5 GeV. The problem of trapping is overcome to a large extent with open boundary and we are able to extract the glueball mass at even larger lattice scale ≈ 5.7 GeV. To smoothen the gauge fields we have used recently proposed Wilson flow which, compared to HYP smearing, exhibits better systematics in the extraction of glueball mass. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV ≤ 1 a ≤ 5.7 GeV.

The degeneracies of single-centered dyonic $$ \frac{1}{4} $$ 1 4 -BPS black holes (BH) in Type II string theory on K3×T2 are known to be coefficients of certain mock Jacobi forms arising from the Igusa cusp form Φ10. In this paper we present an exact analytic formula for these BH degeneracies purely in terms of the degeneracies of the perturbative $$ \frac{1}{2} $$ 1 2 -BPS states of the theory. We use the fact that the degeneracies are completely controlled by the polar coefficients of the mock Jacobi forms, using the Hardy-Ramanujan-Rademacher circle method. Here we present a simple formula for these polar coefficients as a quadratic function of the $$ \frac{1}{2} $$ 1 2 -BPS degeneracies. We arrive at the formula by using the physical interpretation of polar coefficients as negative discriminant states, and then making use of previous results in the literature to track the decay of such states into pairs of $$ \frac{1}{2} $$ 1 2 -BPS states in the moduli space. Although there are an infinite number of such decays, we show that only a finite number of them contribute to the formula. The phenomenon of BH bound state metamorphosis (BSM) plays a crucial role in our analysis. We show that the dyonic BSM orbits with U-duality invariant ∆ < 0 are in exact correspondence with the solution sets of the Brahmagupta-Pell equation, which implies that they are isomorphic to the group of units in the order ℤ[$$ \sqrt{\left|\Delta \right|} $$ Δ ] in the real quadratic field ℚ($$ \sqrt{\left|\Delta \right|} $$ Δ ). We check our formula against the known numerical data arising from the Igusa cusp form, for the first 1650 polar coefficients, and find perfect agreement.