Holographic {\cal N}=1 supersymmetric membrane flows

Ahn, Changhyun; Woo, Kyungsung

doi:10.1088/0264-9381/27/20/205011

Cited by 3 publications

(6 citation statements)

References 62 publications

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“…Since the AdS/CFT correspondence has been extended to other dimensions not only for the duality between an AdS 5 supergravity and a CFT 4 [5,6,7,8,9], it is interesting to study holographic RG flows in these extensions as well. Until now, a lot of works on holographic RG flows in three and four dimensional gauged supergravities have appeared, see for example [10], [11], [12], [13] and [14].…”

Section: Introductionmentioning

confidence: 99%

Holographic RG flows in six dimensional F(4) gauged supergravity

Karndumri

2013

J. High Energ. Phys.

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Abstract:We study critical points of F (4) gauged supergravity in six dimensions coupled to three vector multiplets. Scalar fields are described by R + × SO(4,3) SO(4)×SO (3) coset space, and the gauge group is given by SO(3) R × SO(3) with SO(3) R being the R-symmetry. The maximally supersymmetric critical point with all scalars vanishing preserves the full SO(3) R × SO(3) symmetry. This is dual to a superconformal field theories (SCFT 5 ) arising from a near horizon geometry of the D4-D8 brane system in type I ′ theory with an enhanced global symmetry E 1 ∼ SU(2). Apart from this trivial critical point, we identify a new supersymmetric critical point preserving the full supersymmetry with the SO(3) R × SO(3) symmetry broken to its diagonal subgroup. This critical point should correspond to a new SCFT in five dimensions. We study an RG flow solution interpolating between the SCFT with E 1 symmetry and the new supersymmetric critical point. The flow describes a supersymmetric deformation driven by a vacuum expectation value of relevant operators of dimension 3. We identify the dual operators with the mass terms for hypermultiplet scalars in the dual field theory. The solution provides an example of analytic supersymmetric RG flows in AdS 6 /CFT 5 correspondence.

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Section: Introductionmentioning

confidence: 99%

Holographic RG flows in six dimensional F(4) gauged supergravity

Karndumri

2013

J. High Energ. Phys.

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“…So far we have considerd only some part of membrane flows. The known supersymmetric membrane flows are given by G 2 invariant flow and SU(3)×U(1) R invariant flow [6,27]. These are 11-dimensional lifts of 4-dimensional domain wall solutions in [27,28].…”

Section: Discussionmentioning

confidence: 99%

“…Now we move on the matrix elements of [D 4 , D 5 ] in (E.6). The nonzero expressions of them are summarized by the following matrix elements (1, 2), (2,17), (3,4), (4,19), (5,22), (6, 5), (7,24), (8, 7), (9, 10), (9,26), (11,12), (11,28), (14,13), (14,29), (16,15), (16,31), (17,18), (18,1), (19,20), (20,3), (21,6), (22,21), (23,8), (24,23), (25,10), (25,26), (27,12), (27,28), (30,...…”

Section: Appendix E the Supersymmetry Transformation For 11dimensionamentioning

confidence: 99%

“…(E.8) Furthermore, the following nonzero matrix elements (1,23), (2,24), (3,21), (4,22), (5, 3), (6, 4), (7, 1), (8,2), (13,11), (13,27), (14,12), (14,28), (15,9), (15,25), (16,10), (16,26), (17,7), (18,8), (19,5), (20,6), (21,19), (22,20), (23,17), (24,18), (29,11), (29,27), (30,12), (30,28), (31,…”

Section: Appendix E the Supersymmetry Transformation For 11dimensionamentioning

confidence: 99%

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Towards New Membrane Flow From De Wit–nicolai Construction

Ahn

Paeng

Woo

2012

Int. J. Mod. Phys. A

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The internal 4-form field strengths with 7-dimensional indices have been constructed by de Wit and Nicolai in 1986. They are determined by the following six quantities: the 56-bein of 4-dimensional N = 8 gauged supergravity, the Killing vectors on the round seven-sphere, the covariant derivative acting on these Killing vectors, the warp factor, the field strengths with 4-dimensional indices and the 7-dimensional metric.In this paper, by projecting out the remaining mixed 4-form field strengths in an SU (8) tensor that appears in the variation of spin-1 2 fermionic sector, we also write down them explicitly in terms of some of the above quantities. For the known critical points, the N = 8 SO(8) point and the nonsupersymmetric SO(7) + point, we reproduce the corresponding 11-dimensional uplifts by computing the full nonlinear expressions. Moreover, we find out the 11-dimensional lift of the nonsupersymmetric SO(7) + invariant flow. We decode their implicit formula for the first time and the present work will provide how to obtain the new supersymmetric or nonsupersymmetric membrane flows in 11 dimensions.

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“…Therefore, either one should find the CP 3 -basis around N = 1 IR fixed point, or one needs to find S 6 -basis around N = 2 IR fixed point. Recently, the latter is studied in [32]. Now then we are left with the former.In this paper, we find out an exact solution of N = 1 G 2 -invariant flow (connecting from the N = 8 SO(8) UV fixed point to N = 1 G 2 IR fixed point) to the 11-dimensional Einstein-Maxwell equations where the internal space contains the CP 2 space.…”

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confidence: 99%

Towards an N=1SU(3)-invariant supersymmetric membrane flow in eleven-dimensional supergravity

Ahn

Woo

2012

Journal of Geometry and Physics

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The M-theory lift of N = 1 G 2 -invariant RG flow via a combinatoric use of the 4dimensional RG flow and 11-dimensional Einstein-Maxwell equations was found some time ago. The 11-dimensional metric, a warped product of an asymptotically AdS 4 space with a squashed and stretched 7-sphere, for SU(3)-invariance was found before. In this paper, by choosing the 4-dimensional internal space as CP 2 space, we discover an exact solution of N = 1 G 2 -invariant flow to the 11-dimensional field equations. By an appropriate coordinate transformation on the three internal coordinates, we also find an 11-dimensional solution of N = 1 G 2 -invariant flow interpolating from N = 8 SO(8)-invariant UV fixed point to N = 1 G 2 -invariant IR fixed point. In particular, the 11-dimensional metric and 4-forms at the N = 1 G 2 fixed point for the second solution will provide some hints for the 11-dimensional lift of whole N = 1 SU(3) RG flow connecting this N = 1 G 2 fixed point to N = 2 SU(3) × U(1) R fixed point in 4-dimensions. the RG flows [5], we focus on the G 2 -invariant sector (which is a subset of above SU(3)invariant sector) in 4-dimensional viewpoint by constraining the four arbitrary supergravity fields together with the particular condition. There exist a supersymmetric N = 1 G 2 critical point and two nonsupersymmetric SO(7) ± critical points [29,30] in this sector. If we take the different constraints on the supergravity fields, then we are led to the SU(3) × U(1) Rinvariant sector where there are a supersymmetric N = 2 SU(3) × U(1) R critical point and a nonsupersymmetric SU(4) − critical point [31].The 11-dimensional metric is found by [26] where the compact 7-dimensional metric and warp factor are completely determined in local frames. The two geometric parameters, by constraints, that are nothing but the above supergravity fields, depend on the AdS 4 radial 2 coordinate and are subject to the RG flow equations [7,5] in 4-dimensional gauged supergravity. The global coordinates for S 7 appropriate for the base six-sphere S 6 ≃ G 2 SU (3) preserve the Fubini-Study metric on CP 2 and this describes the ellipsoidally deformed S 7 [25]. On the other hand, by using the relation to the Hopf fibration on CP 3 ≃ SU (4) SU (3)×U (1) explicitly and keeping only the CP 2 space, one can change the remaining three local frames in 7-dimensional manifold via an orthogonal transformation [26]. Each global coordinates depends on each base six-spheres they use.What is the 11-dimensional lift of holographic N = 1 supersymmetric SU (3)-invariant RG flow [13] connecting from N = 1 G 2 critical point to N = 2 SU(3) × U(1) R critical point? At each critical point, the 4-forms are known in different background. Along the supersymmetric RG flow, one expects that there exist the extra 4-forms which should vanish at the critical points. In order to describe the whole RG flow, one needs to have the consistent background.Around N = 2 SU(3) × U(1) R IR fixed point, the use of global coordinates for Hopf fibration on CP 3 was done in [8]. Around N =...

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Holographic {\cal N}=1 supersymmetric membrane flows

Cited by 3 publications

References 62 publications

Holographic RG flows in six dimensional F(4) gauged supergravity

Holographic RG flows in six dimensional F(4) gauged supergravity

Towards New Membrane Flow From De Wit–nicolai Construction

Towards an N=1SU(3)-invariant supersymmetric membrane flow in eleven-dimensional supergravity

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