Flux compactifications in string theory: A Comprehensive review

The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field, assuming only a knowledge of quantum field theory and general relativity. It also forms a comprehensive review, covering the range of ideas that are part of the field, from the Weak Gravity Conjecture, through compactifications of String Theory, to the de Sitter conjecture.

The Swampland: Introduction and Review

The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field, assuming only a knowledge of quantum field theory and general relativity. It also forms a comprehensive review, covering the range of ideas that are part of the field, from the Weak Gravity Conjecture, through compactifications of String Theory, to the de Sitter conjecture.

We perform a systematic search for = 1 Minkowski vacua of type II string theories on compact six-dimensional parallelizable nil- and solvmanifolds (quotients of six-dimensional nilpotent and solvable groups, respectively). Some of these manifolds have appeared in the construction of string backgrounds and are typically called twisted tori. We look for vacua directly in ten dimensions, using the a reformulation of the supersymmetry condition in the framework of generalized complex geometry. Certain algebraic criteria to establish compactness of the manifolds involved are also needed. Although the conditions for preserved = 1 supersymmetry fit nicely in the framework of generalized complex geometry, they are notoriously hard to solve when coupled to the Bianchi identities. We find solutions in a large-volume, constant-dilaton limit. Among these, we identify those that are T-dual to backgrounds of IIB on a conformal T6 with self-dual three-form flux, and hence conceptually not new. For all backgrounds of this type fully localized solutions can be obtained. The other new solutions need multiple intersecting sources (either orientifold planes or combinations of O-planes and D-branes) to satisfy the Bianchi identities; the full list of such new solution is given. These are so far only smeared solutions, and their localization is yet unknown. Although valid in a large-volume limit, they are the first examples of Minkowski vacua in supergravity which are not connected by any duality to a Calabi-Yau. Finally, we discuss a class of flat solvmanifolds that may lead to AdS4 vacua of type IIA strings.

https://iopscience.iop.org/article/10.1088/1126-6708/2007/05/031/pdf

A scan for new N = 1 vacua on twisted tori

http://inspirehep.net/record/787617/files/arXiv:0806.1245.pdf

Ekpyrotic and cyclic cosmology

We study the conditions to have supersymmetric D-branes on general {\cal N}=1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU(3)\times SU(3) structure on T_M\oplus T^\star_M, and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.

Supersymmetric D-branes and calibrations on general N=1 backgrounds

We study the conditions to have supersymmetric D-branes on general = 1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU(3) × SU(3) structure on TM⊕TM, and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.

Supersymmetric D-branes and calibrations on general Script N = 1 backgrounds

We derive a general form of first-order flow equations for extremal and non-extremal, static, spherically symmetric black holes in theories with massless scalars and vectors coupled to gravity. By rewriting the action as a sum of squares a la Bogomol'nyi, we identify the function governing the first-order gradient flow, the `generalised superpotential', which reduces to the `fake superpotential' for non-supersymmetric extremal black holes and to the central charge for supersymmetric black holes. For theories whose scalar manifold is a symmetric space after a timelike dimensional reduction, we present the condition for the existence of a generalised superpotential. We provide examples to illustrate the formalism in four and five spacetime dimensions.

First-order flow equations for extremal and non-extremal black holes

Using the embedding tensor formalism we give the general conditions for the existence of N=1 vacua in spontaneously broken N=2 supergravities. Our results confirm the necessity of having both electrically and magnetically charged multiplets in the spectrum, but also show that no further constraints on the special Kahler geometry of the vector multiplets arise. The quaternionic field space of the hypermultiplets must have two commuting isometries, and as an example we discuss the special quaternionic-Kahler geometries which appear in the low-energy limit of type II string theories. For these cases we find the general solution for stable Minkowski and AdS N=1 vacua, and determine the charges in terms of the holomorphic prepotentials. We find that the string theory realisation of the N=1 Minkowski vacua requires the presence of non-geometric fluxes, whereas they are not needed for the AdS vacua. We also argue that our results should hold in the presence of spacetime and worldsheet instanton corrections.

Spontaneous N=2 to N=1 Supersymmetry Breaking in Supergravity and Type II String Theory

Using the embedding tensor formalism we give the general conditions for the existence of \( \mathcal{N} \) = 1 vacua in spontaneously broken \( \mathcal{N} \) = 2 supergravities. Our results confirm the necessity of having both electrically and magnetically charged multiplets in the spectrum, but also show that no further constraints on the special Kahler geometry of the vector multiplets arise. The quaternionic field space of the hypermultiplets must have two commuting isometries, and as an example we discuss the special quaternionic-Kahler geometries which appear in the low-energy limit of type II string theories. For these cases we find the general solution for stable Minkowski and AdS \( \mathcal{N} \) = 1 vacua, and determine the charges in terms of the holomorphic prepotentials. We find that the string theory realisation of the \( \mathcal{N} \) = 1 Minkowski vacua requires the presence of non-geometric fluxes, whereas they are not needed for the AdS vacua. We also argue that our results should hold in the presence of spacetime and worldsheet instanton corrections.

Paul Smyth

Papers

Supersymmetric D-branes and calibrations on general N=1 backgrounds

Supersymmetric D-branes and calibrations on general Script N = 1 backgrounds

First-order flow equations for extremal and non-extremal black holes

Spontaneous N=2 to N=1 Supersymmetry Breaking in Supergravity and Type II String Theory

Spontaneous $$ \mathcal{N} $$ = 2 → $$ \mathcal{N} $$ = 1 supersymmetry breaking in supergravity and type II string theory