D = 11 Supermembrane instantons,W∞ strings and the super Toda molecule

Castro, Carlos

doi:10.1016/0960-0779(95)00003-8

Cited by 14 publications

(17 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We will see that this limit is connected to W Geometry. We have shown in [22 ] that SU (N ) Self Dual YM in flat 4D spaces, in the large N = ∞ limit, was given by an effective D = 6-dim theory. A dimensional reduction from D = 6 → D = 4 that involved a mixing of " colour " degrees of freedom and spatial ones ( mixing of colour and spacetime coordinates ) furnished Plebanski equations for 4D Self Dual Gravity.…”

Section: The Large N Limit Of Su (N ) Ym In Curved Backgroundsmentioning

confidence: 99%

See 1 more Smart Citation

On the Large N Limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field Theories

Castro¹

2004

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

It is shown that the large N limit of SU (N ) YM in curved m-dim backgrounds can be subsumed by a higher m + n dimensional gravitational theory which can be identified to an m-dim generally invariant gauge theory of diffs N , where N is an n-dim internal space ( Cho, Sho, Park, Yoon ). Based on these findings, a very plausible geometrical interpretation of the AdS/CF T correspondence could be given. Conformally invariant sigma models in D = 2n dimensions with target non-compact SO(2n, 1) groups are reviewed. Despite the non-compact nature of the SO(2n, 1) , the classical action and Hamiltonian are positive definite. Instanton field configurations are found to correspond geometrically to conformal "stereographic" mappings of R 2n into the Euclidean signature AdS 2n spaces. The relation between Self Dual branes and Chern-Simons branes , High Dimensional Knots , follows. A detailed discussion on W ∞ symmetry is given and we outline the Vasiliev procedure to construct an action involving higher spin massless fields in AdS 4 . This AdS 4 spacetime higher spin theory should have a one-to-one correspondence to noncritical W ∞ strings propagating on AdS 4 × S 7 .

show abstract

Section: The Large N Limit Of Su (N ) Ym In Curved Backgroundsmentioning

confidence: 99%

“…( ii ) The effective 3D higher conformal spin field theory of W ∞ strings is related to the 3D continuous SU (∞)(SL(∞)) Toda theory obtained from a Killing symmetry reduction of 4D Self Dual Gravity [22,36] . And the latter can be obtained from the SU (∞) SDYM equations in four-dimensions [ 22 ] .…”

Section: W Geometry and W ∞ Stringsmentioning

confidence: 99%

On the Large N Limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field Theories

Castro¹

2004

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

show abstract

“…The purpose of this subsection is to review our proof [66] that non-critical W ∞ (super) strings are devoid of BRST anomalies in dimensions D = 27, 11, respectively, and which coincide with the the critical (super) membrane dimensions D = 27, 11 found by [69], [70]. We deem this review important due to the relationship between the large N limit of Self-Dual SU (N ) Yang-Mills and Self Dual Gravity [71].…”

Section: Non-critical W ∞ (Super) Strings and The Critical (Super) Mementioning

confidence: 99%

“…In section 5 we will review the interplay among quantum membranes, the continuous Toda theories and non-critical W ∞ (super) strings [66] to show why non-critical W ∞ (super) strings in D = 27(11) dimensions are devoid of BRST anomalies. Such D = 27(11) dimensions coincide with the alleged critical dimensions of the quantum (super) membrane, respectively.…”

mentioning

confidence: 99%

STRINGS AND MEMBRANES FROM EINSTEIN GRAVITY, MATRIX MODELS AND W_∞ GAUGE THEORIES AS PATHS TO QUANTUM GRAVITY

Castro

2008

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

It is shown how w∞, w1+∞ Gauge Field Theory actions in 2D emerge directly from 4D Gravity. Strings and Membranes actions in 2D and 3D originate as well from 4D Einstein Gravity after recurring to the nonlinear connection formalism of Lagrange-Finsler and Hamilton-Cartan spaces. Quantum Gravity in 3D can be described by a W∞ Matrix Model in D = 1 that can be solved exactly via the Collective Field Theory method. We describe why a quantization of 4D Gravity could be attained via a 2D Quantum W∞ gauge theory coupled to an infinite-component scalar-multiplet. A proof that non-critical W∞ (super) strings are devoid of BRST anomalies in dimensions D = 27 (D = 11), respectively, follows and which coincide with the critical (super) membrane dimensions D = 27 (D = 11). We establish the correspondence between the states associated with the quasi finite highest weights irreducible representations of W∞,W∞ algebras and the quantum states of the continuous Toda molecule. Schroedinger-like QM wave functional equations are derived and solutions are found in the zeroth order approximation. Since higher-conformal spin W∞ symmetries are very relevant in the study of 2D W∞ Gravity, the Quantum Hall effect, large N QCD, strings, membranes, ...... it is warranted to explore further the interplay among all these theories. In this introductory section we will review the work of [2] and afterwards we will discuss the recent work related the Hidden Symmetries of M theory. Keywords1.1 Gravity in D = m + n as an m-dim Gauge Theory of diffeomorphisms of an internal n-dim space and HolographySome time ago Park [1] showed that 4D Self Dual Gravity is equivalent to a WZNW model based on the group SU (∞). Namely, 4D Self Dual Gravity is the non-linear sigma model based in 2D whose target space is the "group manifold" of area-preserving diffs of another 2D-dim manifold. Roughly speaking, this means that the effective D = 4 manifold, where Self Dual Gravity is defined, is "spliced" into two 2D-submanifolds: one submanifold is the original 2D base manifold where the non-linear sigma model is defined. The other 2D submanifold is the target group manifold of area-preserving diffs of a two-dim sphere S 2 . The authors [2] went further and generalized this particular Self Dual Gravity case to the full fledged gravity in D = 2 + 2 = 4 dimensions, and in general, to any combinations of m + n-dimensions. Their main result is that m + n-dim Einstein gravity can be identified with an m-dimensional generally invariant gauge theory of Dif f s N , where N is an n-dim manifold. Locally the m + ndim space can be written as Σ = M × N and the metric G AB decomposes as: [62]. The decomposition (1.1) must not be confused with the Kaluza-Klein reduction where one imposes an isometry restriction on the γ AB that turns A a µ into a gauge connection associated with the gauge group G generated by isometry. Dropping the isometry restrictions allows all the fields to depend on all the coordinates x, y. Nevertheless A a µ (x, y) can still be identified as a conne...

show abstract

“…The spatial positions and gauge parameters of the SU(∞) anyons or "chirons" in this model can be reinterpreted [9,10] In order to progress beyond the simple model of ref. 2 we would like first of all to take notice of the fact that the continuous Toda model representation for self-dual membranes has natural realizations in 7+1 dimensions [11,12]. Therefore we are led to the direct product of two 8-dimensional manifolds, or perhaps the complexification of an 8-manifold, as the natural setting for the paired non-linear gravitons appearing in the condensate model of ref.…”

Section: Introductionmentioning

confidence: 99%

A Unique Theory of Gravity and Matter

Chapline

1999

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

The author has previously suggested that the ground state for 4-dimensional quantum gravity can be represented as a condensation of nonlinear gravitons connected by Dirac strings. In this note we suggest that the low-lying excitations of this state can be described by a quasitopological action of the form d z 13 ∫ F 4 ∧ F 5 ∧ F 4 , corresponding to a trilinear coupling of solotonic 8-branes and 7-branes. It is shown that when the excitations associated with F 5 are neglected, the effective action can be interpreted as a theory of conformal gravity in four dimensions. This in turn suggests that ordinary gravity as well supersymmetric matter and phenomenological gauge symmetries arise from the spontaneous breaking of topological invariance. The possibly deep mathematical significance of this theory is also noted.

show abstract

D = 11 Supermembrane instantons,W∞ strings and the super Toda molecule

Cited by 14 publications

References 48 publications

On the Large N Limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field Theories

On the Large N Limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field Theories

STRINGS AND MEMBRANES FROM EINSTEIN GRAVITY, MATRIX MODELS AND W_∞ GAUGE THEORIES AS PATHS TO QUANTUM GRAVITY

A Unique Theory of Gravity and Matter

Contact Info

Product

Resources

About

D = 11 Supermembrane instantons,W∞ strings and the super Toda molecule

Cited by 14 publications

References 48 publications

On the Large N Limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field Theories

On the Large N Limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field Theories

STRINGS AND MEMBRANES FROM EINSTEIN GRAVITY, MATRIX MODELS AND W∞ GAUGE THEORIES AS PATHS TO QUANTUM GRAVITY

A Unique Theory of Gravity and Matter

Contact Info

Product

Resources

About

STRINGS AND MEMBRANES FROM EINSTEIN GRAVITY, MATRIX MODELS AND W_∞ GAUGE THEORIES AS PATHS TO QUANTUM GRAVITY