Non-Geometric Vacua of the Spin(32)/Z2\mathbf{\text{Spin}(32)/\mathbb Z_2} Heterotic String and Little String Theories

We study a class of 6d $\mathcal{N}=(1,0)$ non-geometric vacua of the $\text{Spin}(32)/\mathbb Z_2$ heterotic string which can be understood as fibrations of genus-two curves over a complex one-dimensional base. The 6d $\mathcal{N}=(1,0)$ theories living on the defects that arise when the genus-two fiber degenerates at a point of the base are analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. We consider all possible degenerations of genus-two curves and systematically attempt to resolve the singularities of the dual threefolds. As in the analogous non-geometric vacua of the $E_8\times E_8$ heterotic string, we find that many of the resulting dual threefolds contain singularities which do not admit a crepant resolution. When the singularities can be resolved crepantly, we determine the emerging effective theories which turn out to be little string theories at a generic point on their tensor branch. We also observe a form of duality in which theories living on distinct defects are the same.Comment: 39 pages, 3 figures, and 6 table

Non-geometric heterotic backgrounds and 6D SCFTs/LSTs

We study ${\mathcal N}=(1,0)$ six-dimensional theories living on defects of non-geometric backgrounds of the $E_8\times E_8$ and the $\text{Spin}(32)/{\mathbb Z}_2$ heterotic strings. Such configurations can be analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. The majority of the resulting dual threefolds turn out to contain singularities which do not admit a crepant resolution. When the singularities can be resolved crepantly, the theories living on the defect are explicitly determined and reveal a form of duality in which distinct defects are described by the same IR fixed point. In particular, a subclass of non-geometric defects corresponds to SCFTs/LSTs arising from small heterotic instantons on ADE singularities.Comment: Slightly extended version of the proceedings prepared for the 'Workshop on Geometry and Physics,' November 2016, Ringberg Castle, Germany; 16 page

The Swampland Distance Conjecture and towers of tensionless branes

The Swampland Distance Conjecture states that at infinite distance in the scalar moduli space an infinite tower of particles become exponentially massless. We study this issue in the context of 4d type IIA and type IIB Calabi-Yau compactifications. We find that for large moduli not only towers of particles but also domain walls and strings become tensionless. We study in detail the case of type IIA and IIB = 1 CY orientifolds and show how for infinite Kähler and/or complex structure moduli towers of domain walls and strings become tensionless, depending on the particular direction in moduli space. For the type IIA case we construct the monodromy orbits of domain walls in detail. We study the structure of mass scales in these limits and find that these towers may occur at the same scale as the fundamental string scale or the KK scale making sometimes difficult an effective field theory description. The structure of IIA and IIB towers are consistent with mirror symmetry, as long as towers of exotic domain walls associated to non-geometric fluxes also appear. We briefly discuss the issue of emergence within this context and the possible implications for 4d vacuaThis work has been supported by the ERC Advanced Grant SPLE under contract ERC-2012-ADG-20120216-320421, by the grant FPA2012-32828 from the MINECO, and the grant SEV-2012-0249 of the “Centro de Excelencia Severo Ochoa” Programme. The work of A.H. is supported by the Spanish FPU Grant No. FPU15/05012

On scale separation in type II AdS flux vacua

We study the separation of AdS and Kaluza-Klein (KK) scales in type II 4d AdS orientifold vacua. We first address this problem in toroidal/orbifold type IIA vacua with metric fluxes, corresponding to compactifications in twisted tori, both from the 4d and 10d points of view. We show how the naive application of the effective 4d theory leads to results which violate the AdS distance conjecture, in a class of N = 1 supersymmetric models which have a 10d lifting to a compactification on S3× S3. We show how using KK scales properly modified by the compact metric leads to no separationof scales with MKK2=c|Λ|, with c a numerical constant independent of fluxes. This applies with no need to keep non-leading fluxes fixed. We also consider a class of IIB models with non-geometric fluxes in which the effective field theory analysis seems to lead to a naive separation of scales and a violation of the AdS distance conjecture. It has a T-dual which again may be understood as a 10d type IIA theory compactified on S3× S3. In this geometric dual one again observes that the strong AdS distance conjecture is obeyed with MKK2=c′|Λ|, if one takes into account the curvature in the internal space. These findings seem to suggest that all toroidal/orbifold models with fluxes in this class obey MKK2=c|Λ| with c a flux-independent numerical constantThis work is supported by the Spanish Research Agency (Agencia Estatal de Investigación) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, and by the grants FPA2015- 65480-P and PGC2018-095976-B-C21 from MCIU/AEI/FEDER, UE. A.H. is supported JHEP03(2020)013 by the Spanish FPU Grant No. FPU15/0501

A class of non-supersymmetric orientifolds

We study type IIB orientifolds on T^{2d}/Z_N with supersymmetry broken by the compactification. We determine tadpole cancellation conditions including anti-branes and considering different actions for the parity Omega. Using these conditions we then obtain the spectrum of tachyons and massless states. Various examples with N even correspond to type 0B orientifolds.Comment: 49 pages, Late

Mirror Symmetry for Two Parameter Models -- II

We describe in detail the space of the two K\"ahler parameters of the Calabi--Yau manifold $\P_4^{(1,1,1,6,9)}[18]$ by exploiting mirror symmetry. The large complex structure limit of the mirror, which corresponds to the classical large radius limit, is found by studying the monodromy of the periods about the discriminant locus, the boundary of the moduli space corresponding to singular Calabi--Yau manifolds. A symplectic basis of periods is found and the action of the $Sp(6,\Z)$ generators of the modular group is determined. From the mirror map we compute the instanton expansion of the Yukawa couplings and the generalized $N=2$ index, arriving at the numbers of instantons of genus zero and genus one of each degree. We also investigate an $SL(2,\Z)$ symmetry that acts on a boundary of the moduli space.Comment: 57 pages + 9 figures using eps

Strings on Eight-Orbifolds

We present several examples of T^8/P orbifolds with $P \subset SU(4)$. We compute their Hodge numbers and consider turning on discrete torsion. We then study supersymmetric compactifications of type II, heterotic, and type I strings on these orbifolds. Heterotic compactifications to D=2 have a B-field tadpole with coefficient given by that of the anomaly polynomial. In the SO(32) heterotic with standard embedding the tadpole is absent provided the internal space has a precise value of the Euler number. Guided by their relation to type I, we find tadpole-free SO(32) heterotic orbifolds with non-standard embedding.Comment: 32 pages, Latex, v2: added reference

Periods and Duality Symmetries in Calabi-Yau Compactifications

We derive the period structure of several one-modulus Calabi-Yau manifolds. With this knowledge we then obtain the generators of the duality group and the mirror map that defines the physical variable $t$ representing the radius of compactification. We also describe the fundamental region of $t$ and discuss its relation with automorphic functions. As a byproduct of our analysis we compute the non-perturbative corrections of Yukawa couplings.Comment: (37 pages, one figure not included

Stringy Tachyonic Instabilities of Non-Supersymmetric Ricci Flat Backgrounds

Superstring/M-theory compactified on compact Ricci flat manifolds have recently been conjectured to exhibit instabilities whenever the metrics do not have special holonomy. We use worldsheet conformal field theory to investigate instabilities of Type II superstring theories on compact, Ricci flat, spin 3-manifolds including a worldsheet description of their spin structures. The instabilities are signalled by the appearance of stringy tachyons at small radius and a negative (1-loop) vacuum energy density at large radius. We briefly discuss the extension to higher dimensions.Comment: 30+3p