A scan for new N = 1 vacua on twisted tori

By M. Graña, R. Minasian, M. Petrini, A. Tomasiello. 2006

276 citations recorded by the source corpus.

We perform a systematic search for N = 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 N = 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 T 6 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.

Subfields: Computational Mathematics, Computer Graphics and Computer-Aided Design, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ea591cef979f4305a297c138e89b21cafba4853f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. B. Wecht
2. Eran Palti
3. E. Silverstein
4. Paul Koerber
5. U. Danielsson
6. T. Riet

In Computer Graphics and Computer-Aided Design

1. B. Wecht
2. Eran Palti
3. E. Silverstein
4. Paul Koerber
5. D. Waldram
6. M. Graña
7. A. Tomasiello

In Nuclear and High Energy Physics

1. Eran Palti
2. M. Graña
3. D. Lust
4. Paul Koerber
5. C. Nuñez
6. U. Danielsson
7. Gary Shiu
8. D. Thompson

Citations in the corpus

• All AdS7 solutions of type II supergravity (2013, background): “It can be found by direct computation, or also as a consequence of the system for Mink4×M6 in [7]: one takesM6 = R(2)×M4, with warping A = A4, internal metric ds(2)M6 = e 2A4((dx4)2+ (dx5)2) + ds(2)M4 , and, in the language of [15], Φ1 = e 4(dx(4) + idx(5)) ∧ φ(2)∓ , Φ2 = (1 + ie4dx(4) ∧ dx(5)) ∧ φ(”
• T-duality, generalized geometry and non-geometric backgrounds (2008, result): “For b = 0, the T-dual structure would be a “static SU(2)” (k‖ = 0), in agreement with the examples studied in [27].”
• Towards classical de Sitter solutions in string theory (2009, unknown): “Reference [34] contains an explicit classification of Solvmanifolds which we plan to investigate.”
• Lectures on nongeometric flux compactifications (2007, methodology): “T-duality then gives the set of NS–NS constraints H̄ x[abf x cd] = 0 (5.12) f ax[bf x cd] + H̄ x[bcQ ax d] = 0 (5.13) Q[ab]x f x [cd] − 4f [ax[cQb]xd] + H̄ x[cd]R[ab]x = 0 (5.14) Q[abx Q c]x d + f [a xdR bc]x = 0 (5.15) Q[abx R cd]x = 0.”
• Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes (2008, background): “What will follow in the next section is a (partial) classification of orientifolds of T 6 which preserve N = 1 supersymmetry in four dimensions (see also a related classification in [29]).”
• The Swampland: Introduction and Review (2019, methodology): “he former preserve the symmetry while the latter break it. More generally, consistent truncations can be employed when the compactication manifold has a group, or coset, structure. See, for example, [193,194,196,197] for discussions on this point. We will henceforth denote the compactication as M 6 ”
• The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets (2008, methodology): “A systematic scan yields exactly two possibilities in type IIA, namely the six-torus and the nilmanifold 4.7 of Table 4 of [ 20 ] (also known as the Iwasawa manifold), which (for some values of the parameters) turn out to be related by T-duality along two directions.”
• Simple de Sitter solutions (2007, methodology): “Simple and explicit models of compactification down to AdS4 have been found using this general framework(1) in type IIB string theory [18,19,20] and IIA [14,16,21,15,22].”
• De Sitter hunting in a classical landscape (2011, background): “The second solvable algebra does not appear in the table of [56] and implies that it is not algebraic.”
• Smeared versus localised sources in flux compactifications (2010, background): “The solutions on the twisted tori of [19] were obtained in the smeared limit and a discussion on their localisation was given in [2,3].”
• A simple class of N = 3 gauge/gravity duals (2008, background): “Because of general results on AdS4 solutions [49,50], this means that, from a type IIA perspective, this solution has an SU(3)× SU(3) structure on T ⊕ T ∗ (as opposed to an SU(3) structure on the tangent bundle).”