p -branes from generalized Yang-Mills theory

Abstract

Abstract. We consider the reduced, quenched version of a generalized Yang-Mills action in 4k-dimensional spacetime. This is a new kind of matrix theory which is mapped through the Weyl-Wigner-Moyal correspondence into a field theory over a non-commutative phase space. We show that the "classical" limit of this field theory is encoded into the effective action of an open, (4k−1)-dimensional, bulk brane enclosed by a dynamical, Chern-Simons type, (4k − 2)-dimensional, boundary brane. The bulk action is a pure volume term, while the boundary action carries all the dynamical degrees of freedom.

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

“…2) The validity of eq-(4.2) can also be justified by our results of [29], [30], [31], [32], [33] which showed rigorously why the large N limit of quenched QCD (quenched to a point and a line), after performing a Moyal deformation quantization procedure of the corresponding SU (N ) Yang-Mills theory, furnished string and membrane actions, respectively, in the "classical"h → 0 limit and which was tantamount to the N → ∞ limit sinceh ∼ 1 N . A Moyal quantization procedure of Generalized Yang-Mills theories based on actions involving F ∧ F ∧ F... yielded p-brane actions.…”

“…Such Killing symmetry reduction to 1D is essentially equivalent to the quenching procedure of the large N QCD to a line [31], [32]. The gauge fields/membrane coordinates correspondence is A µ (x 0 , y a ) ↔ X µ (x 0 , y a ).…”

“…The relationship between W ∞ gravity (geometry) and the Fedosov deformation quantization of the 4D Self-Dual Gravity [38] associated with the complexified co-tangent space of a two-dim Riemann surface was studied by [40], [39]. String and p-branes actions can be obtained by a Moyal deformation quantization of (Generalized ) Yang-Mills as shown in [29], [30], [31], [32], [33]. A natural Fedosov type quantization of generalized Lagrange models and gravity theories with metrics lifted on tangent bundle, or extended to higher dimensions, has been attained by Vacaru [60], [61], [62].…”

The QCD M embrane

“…Tracing back the bulk and boundary terms in the original action (1) it is possible to establish the following formal correspondence "glue" ←→ bulk 3-brane "instantons" ←→ Chern-Simons boundary 2-brane. This scheme, which has been generalized to Yang-Mills theories in higher dimensional spacetime [9], points out that not only strings but bag-like objects fit the large-N spectrum of SU(N) gauge theories. However, a non-trivial dynamics for these spacetime filling objects comes only from boundary effects, described by Chern-Simons terms in the original gauge action.…”

“…The model (3) has a rich spectrum of extended objects. Our investigations in [8] and [9] has been initially triggered by the formal analogy between (3) in 10D and quenched Yang-Mills theory in 4D. Matrix description of Type IIA strings is given in terms of 0-branes quantum mechanics…”