D-branes in Yang-Mills theory and Emergent Gauge Symmetry

Abstract

Four-dimensional supersymmetric SU(N) Yang-Mills theory on a sphere has highly charged baryon-like states built from anti-symmetric combinations of the adjoint scalars. We show that these states, which are equivalently described as holes in a free fermi sea of a reduced matrix model, are D-branes. Their excitations are stringlike and effectively realize Dirichlet and Neumann boundary conditions in various directions. The low energy brane dynamics should realize an emergent gauge theory that is local on a new space. We show that the Gauss' Law associated to this emergent gauge symmetry appears from combinatorial identities relating the stringy excitations. Although these excitations are not BPS, they can be near-BPS and we can hope to study them in perturbation theory. Accordingly, we show that the Chan-Paton factors expected for strings propagating on multiple branes arise dynamically, allowing the emergent gauge symmetry to be non-Abelian.

Anomalous dimensions of heavy operators from magnon energies

“…For the systems we are interested in, the most convenient basis to use is provided by the restricted Schur polynomials. Inspired by the Gauss Law which will arise in the world volume description of the giant graviton branes, the authors of [23] suggested operators in the gauge theory that are dual to excited giant graviton brane states. This inspired idea was pursued both in the case that the open strings are described by an open string word [24][25][26] and in the case of minimal open strings, with each open string represented by a single magnon [27,28].…”

(Non)-integrability of geodesics in D-brane backgrounds

“…The interactions between these objects can be very complicated [25][26][27], but additional simplifications occur for semiclassical configurations of giant gravitons with J ∼ N 2 , which can be viewed as classical geometries [28]. In this regime of parameters, integrability of the sector (1.2) reduces to integrability of strings on the bubbling geometries constructed in [28].…”

“…Since equation (5.9) is analytic in these parameters, separability must persist even in the unphysical region where M = 0 and N is arbitrary. 25 In this region, equation (5.3) reduces to (3.26) with H → H 2 , p µ p µ → N 2 , then arguments presented in section 3.1 reduce the problem to H 2 (r, θ) with base space 5) and the analysis of section 3.2 leads to three possible solutions ((3.50), (3.51), (3.52)) for (x, y) and H 2 . Let us now demonstrate that H 1 can only be a function of r and θ.…”

BPSR-balls in Script N = 4 SYM onR×S3, quantum Hall analogy and AdS/CFT holography

“…This is in accordance with ref. [20]. In the same limit, the gaugino and gluon backgrounds are decoupled from this sector too [16].)…”

“…Applying the above results to our matrix model (6.14), we have 20) where k is an integer, and (p, q) is again a coprime pair defined by the ratio N 2 /N 1 = q/p. Substituting the quantized θ into eq.…”