Mink3 × S3 solutions of type II supergravity

2019

J. High Energ. Phys.

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New local solutions in type II supergravity that are foliations of AdS 3 × S 3 × S 3 over an interval and preserve at least large N = (4, 0) supersymmetry are found. Some cases have compact internal space, some not and one experiences an enhancement to N = (4, 4). We present two new globally compact solutions with D brane and O plane sources explicitly, one in each of IIA and IIB. The former is part of an infinite family of solutions with D8/O8s back reacted on AdS 3 × S 3 × S 3 × S 1 . In the latter the the algebra degenerates to small N = (4, 0) and the internal geometry is bounded between D5s and O5s back reacted on AdS 3 × S 3 × R 4 .

Section: Introductionmentioning

confidence: 83%

“…This time ν |ν| = ±1 parametrise a spinor charged under the SU(2) L/R subgroup of SO(4) ∼ = SU(2) L ×SU(2) R that are singlets under the SU(2) R/L . As shown in [34], in the Hopf fibration frame of We parametrise these in a unified language as K i such that…”

Section: Introductionmentioning

confidence: 99%

Type II solutions on AdS3 × S3 × S3 with large superconformal symmetry

2019

J. High Energ. Phys.

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“…for a = 1, 2. Here a 1,2 are SU(2) doublets on S 3 1,2 (see [37] for details) defined in terms of the 3-sphere Killing spinors as The SO(4) R-symmetry is embedded in SO(4)×SO(4) as follows: the 3-sphere S 3 1,2 admits a global SO(4) 1,2 ∼SU(2) 1,2+ × SU(2) 1,2,− isometry. Let us assume for simplicity that = 1 5 so that 1,2 is charged under SU(2) 1,2+ , the SO(4) R-symmetry is then…”

Section: )mentioning

confidence: 99%

“…which is computed in [37]. This is necessary in the derivation of Ψ ± which decomposes as in terms of wedge products of bispinors on the two S 3 and the interval direction.…”

Section: Partially Breaking  = (4 0) With An S 3 ×S 3 Fibrationmentioning

confidence: 99%

AdS₃ solutions with from S³ × S³ fibrations

Legramandi

Fortschritte der Physik

2020

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We study warped AdS 3 solutions in massive IIA supergravity preserving  = (3, 0) and  = (1, 0) supersymmetry. We consider solutions whose internal spaces decompose as an S 3 ×S 3 fibration and a interval over which the rest of the solution is foliated. We present necessary and sufficient conditions for these solutions to exist, in terms of systems of ordinary differential equations and find several new analytic and numerical examples with internal spaces bounded between D-brane and O-plane behaviors.1 Interestingly [32] find  = (8, 0) solutions in 3d gauged supergravity that do not appear to be able to be embedded in 10 or 11 dimensionsso this may not be the full story.

“…Most progress constructing compact solutions with fluxes has happened within another restrictive ansatz, with the internal space assumed to be conformally a holonomy manifold [21][22][23], allowing one to broadly use the same mathematical tools as before. At this point all Mink d solutions for d > 1 (with the exception of Mink 2 in eleven dimensions) have been classified (see [24][25][26][27][28] for eleven dimensions, [29][30][31][32][33][34][35][36] for ten dimensions), however finding solutions beyond the ansatz of warped holonomy has proved challenging -see [38,39] for success in this direction. The issue appears to be one of tractability, so it would be helpful to have some additional guiding principle.AdS solutions necessitate the inclusion of fluxes, early examples were also constructed by studying warped holonomy manifolds (albeit now non compact) using the Freund-Rubin ansatz [40].…”

mentioning

confidence: 99%

Mink4 × S2 solutions of 10 and 11 dimensional supergravity

Legramandi

2019

J. High Energ. Phys.

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We complete the classification of Mink 4 solutions preserving N = 2 supersymmetry and SU(2) Rsymmetry parameterised by a round S 2 factor. We consider eleven-dimensional supergravity and relax the assumptions of earlier works in type II theories. We show that, using chains of dualities, all solutions of this type can be generated from one of two master classes: an SU(2)-structure in M-theory and a conformal Calabi-Yau in type IIB. Finally, using our results, we recover AdS 5 × S 2 solutions in M-theory and construct a compact Minkowski solution with Atiyah-Hitchin singularity. IntroductionSome of the most physically relevant solutions in supergravity are those exhibiting a warped Minkowski factor. From early on, the main reason for this is that Minkowski vacua of string and M-theory are required to make contact with known particle physics phenomena in four dimensions, where one should arrange for the co-dimensions to be compact. Another reason, which clearly gained considerable traction with the advent of the AdS/CFT correspondence, is that all AdS solutions admit a description in terms of a foliation of Minkowski over a non compact interval -namely the Poincaré patch.The most simple way to realise a Minkowski vacua from ten or eleven dimensions is to assume that the compact internal space accommodates some holonomy group, specifically SU(3) or G 2 for compactifications of string theory or M-theory down to four dimensions respectively. Such solutions preserve (at least) N = 2 supersymmetry and have been well studied in the literature [1][2][3][4][5], with a resurgence of interest in the G 2 case in recent years [6-9] (see also [10][11][12][13] for G 2 arising in a heterotic context). However, such manifolds support neither fluxes nor a warping of the Minkowski directions, so it is reasonable to expect that they represent a rather small region of the space of possible solutions. The inclusion of fluxes requires one to generalise the notion of holonomy group to structure group (or G-structure) [14][15][16][17]. It is well known that no compact regular solutions of this type exist [18-20] -indeed a necessary element of such constructions are localised singularities, namely O-planes and their generalisations through string dualities, or lifts to M-theory (e.g. Atiyah-Hitchin singularities). Most progress constructing compact solutions with fluxes has happened within another restrictive ansatz, with the internal space assumed to be conformally a holonomy manifold [21][22][23], allowing one to broadly use the same mathematical tools as before. At this point all Mink d solutions for d > 1 (with the exception of Mink 2 in eleven dimensions) have been classified (see [24][25][26][27][28] for eleven dimensions, [29][30][31][32][33][34][35][36] for ten dimensions), however finding solutions beyond the ansatz of warped holonomy has proved challenging -see [38,39] for success in this direction. The issue appears to be one of tractability, so it would be helpful to have some additional guiding principle.AdS solutions necessita...