β-deformation for matrix model of M-theory

Shimada, Hidehiko

doi:10.1016/j.nuclphysb.2008.08.018

Cited by 9 publications

(7 citation statements)

References 83 publications

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“…In other setups, to argue for the genus of the surface is more involved, using an approximation to Morse theory on the surface [30], and the result is inherently more fuzzy, or explicitly requires taking a limit of large matrices [32]. One can also obtain more standard fuzzy tori as zero energy configurations in higher dimensions by studying beta deformed matrix models [31].…”

Section: B From a Sphere To A Torusmentioning

confidence: 99%

Matrix embeddings on flatR3and the geometry of membranes

2012

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We show that given three hermitian matrices, what one could call a fuzzy representation of a membrane, there is a well defined procedure to define a set of oriented Riemann surfaces embedded in R 3 using an index function defined for points in R 3 that is constructed from the three matrices and the point. The set of surfaces is covariant under rotations, dilatations and translation operations on R 3 , it is additive on direct sums and the orientation of the surfaces is reversed by complex conjugation of the matrices. The index we build is closely related to the Hanany-Witten effect.We also show that the surfaces carry information of a line bundle with connection on them. We discuss applications of these ideas to the study of holographic matrix models and black hole dynamics.

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Section: B From a Sphere To A Torusmentioning

confidence: 99%

Matrix embeddings on flatR3and the geometry of membranes

2012

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“…In the context of Matrix theory, this deformation is considered in [21] and the stable membrane solutions of different topology are studied in the continuum limit. It will be certainly very interesting to consider BPS objects with different dimensions in the matrix models described in this paper.…”

Section: Discussionmentioning

confidence: 99%

“…For 10 dimensional IIB supergravity, pp-waves on special holonomy manifolds are studied and it is shown that the Ramond-Ramond 5-form induces a superpotential on the light cone worldsheet Lagrangian [18], while the 3-forms are responsible for Killing vector potentials [19]. More recently, inspired by [20], supersymmetric Matrix models with so-called β-deformation are studied [21], and it is illustrated that the deformation superpotential of the discretized supermembrane action is given by inhomogeneous background fluxes which have a linear dependence on transverse coordinates. It is this discovery which motivated our research on ppwaves with a generic superpotential reported in this paper.…”

Section: Introductionmentioning

confidence: 99%

ℓ-theory on pp-waves with a holomorphic superpotential and its membrane and matrix descriptions

Kim¹,

Kim²,

Park³

et al. 2008

J. High Energy Phys.

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We study a new class of inhomogeneous pp-wave solutions with 8 unbroken supersymmetries in D = 11 supergravity. The 9 dimensional transverse space is Euclidean and split into 3 and 6 dimensional subspaces. The solutions have non-constant gauge flux, which are described in terms of an arbitrary holomorphic function of the complexified 6 dimensional space. The supermembrane and matrix theory descriptions are also provided and we identify the relevant supersymmetry transformation rules. The action also arises through a dimensional reduction of N = 1, D = 4 supersymmetric Yang-Mills theory coupled to 3 gauge adjoint and chiral multiplets, whose interactions are determined by the holomorphic function of the supergravity solution now constituting the superpotential.

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“…A comprehensive review can be found in [12]. In this paper we follow the conventions of [67]. Functions on the membrane world-volume at fixed time, f (σ 1 , σ 2 ), g(σ 1 , σ 2 ), .…”

Section: )mentioning

confidence: 99%

“…The possibility of interpreting the block offdiagonal components in the pp-wave matrix model as the non-Abelian degrees of freedom of membranes was suggested in[28]. In[67] it was pointed out that the non-Abelian nature of membranes may explain certain interesting properties of stable solutions (corresponding to membranes with torus topology) in a deformed version of the matrix model, where configurations of membranes characterised by different winding numbers in the continuum theory become indistinguishable in the matrix model description.…”

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confidence: 99%

Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3

Kovacs¹,

Sato²,

Shimada³

2014

Progress of Theoretical and Experimental Physics

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We consider states with large angular momentum to facilitate the study of the Mtheory regime of the AdS 4 /CFT 3 correspondence. More precisely, we study the duality between M-theory on AdS 4 × S 7 / k and N = 6 supersymmetric Chern-Simons-matter (ABJM) theory with gauge group U(N )×U(N ) and level k, in the regime where k is of order one and N is large. In this regime the study of both sides of the duality is challenging: the lack of an explicit formulation of M-theory in AdS 4 × S 7 / k makes the gravity side difficult, while the CFT side is strongly coupled and the planar approximation is not applicable. In order to overcome these difficulties, we focus on states on the gravity side with large orbital angular momentum J ≫ 1 associated with a single plane of rotation in S 7 . We then identify the corresponding operators in the CFT, thereby establishing the AdS/CFT dictionary in this large angular momentum sector. We show that there are natural approximation schemes on both sides of the correspondence as a consequence of the presence of the small parameter 1/J. On the AdS side, the sector we focus on is well-approximated by the matrix model of M-theory -with matrices of size J/kdefined on the maximally supersymmetric eleven-dimensional pp-wave background. The pp-wave approximation to M-theory in AdS 4 ×S 7 / k is justified for 1 ≪ J ≪ N 1/2 , while loop corrections in the matrix model are suppressed compared to tree-level contributions for J ≫ N 1/3 . On the CFT side, we study the ABJM theory defined on S 2 × Ê with large magnetic flux J/k. Using a carefully chosen gauge, we find an expansion of the Born-Oppenheimer type which arises naturally for large J in spite of the theory being strongly coupled. The energy spectra computed on the two sides agree at leading order. This provides a highly non-trivial test of the AdS 4 /CFT 3 correspondence including near-BPS observables associated with membrane degrees of freedom, therefore extending the validity of the AdS 4 /CFT 3 duality beyond the previously studied sectors corresponding to either BPS supergravity observables or the type IIA string regime.for the applicability of the pp-wave approximation.After describing the ground state in the large J sector, we discuss the spectrum of fluctuations around the classical vacuum configurations following [28][29][30]. We present the tree level spectrum, which is determined by the pp-wave matrix model Hamiltonian at quadratic order in the fluctuations. We then discuss the behaviour of quantum corrections associated with cubic and quartic terms in the fluctuations 3 . The condition that one-loop effects produce small corrections to the tree level result turns out to be J ≫ N 1/3 .( 1.2) It is crucial for our proposal that both conditions, (1.1) and (1.2), can be satisfied for large N choosing the parameter J so thatHaving discussed the large angular momentum sector on the gravity side using the ppwave matrix model, we then describe the dual large J observables in the CFT. These are gauge-invariant operators in the ABJM theory...

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β-deformation for matrix model of M-theory

Cited by 9 publications

References 83 publications

Matrix embeddings on flatR3and the geometry of membranes

Matrix embeddings on flatR3and the geometry of membranes

ℓ-theory on pp-waves with a holomorphic superpotential and its membrane and matrix descriptions

Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3

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