Notes on Collective Field Theory of Matrix and Spin Calogero Models

Matrix models and related Spin-Calogero-Sutherland models are of major relevance in a variety of subjects, ranging from condensed matter physics to QCD and low dimensional string theory. They are characterized by integrability and exact solvability. Their continuum, field theoretic representations are likewise of definite interest. In this paper we describe various continuum, field theoretic representations of these models based on bosonization and collective field theory techniques. We compare various known representations and describe some nontrivial applications.Comment: 36 pages, no figures v2: references added, a version to appear in the special issue of JPhysA (edited by G Dunne, J Feinberg and P Dorey) v3:comments changed, paper identical to v

Thermofield Duality for Higher Spin Rindler Gravity

We study the Thermo-field realization of the duality between the Rindler-AdS higher spin theory and $O(N)$ vector theory. The CFT represents a decoupled pair of free $O(N)$ vector field theories. It is shown how this decoupled domain CFT is capable of generating the connected Rindler-AdS background with the full set of Higher Spin fields.Comment: 23 pages, 1 figure; v2 reference added; v3 presentation modified and typos correcte

String field actions from W-infinity

Starting from $W_{\infty}$ as a fundamental symmetry and using the coadjoint orbit method, we derive an action for one dimensional strings. It is shown that on the simplest nontrivial orbit this gives the single scalar collective field theory. On higher orbits one finds generalized KdV type field theories with increasing number of components. Here the tachyon is coupled to higher tensor fields.Comment: 18 page

Bulk from Bi-locals in Thermo Field CFT

We study the Large $N$ dynamics of the $O(N)$ field theory in the Thermo field dynamics approach. The question of recovering the high temperature phase and the corresponding $O(N)$ gauging is clarified. Through the associated bi-local representation we discuss the emergent bulk space-time and construction of (Higher spin) fields. We note the presence of `evanescent' modes in this construction and also the mixing of spins at finite temperature.Comment: 24 page. v2: references added, minor corrections. v3: typo corrected, clarification added, conclusion revised, version to appear in JHE

Non commutative gravity from the ADS/CFT correspondence

The exclusion principle of Maldacena and Strominger is seen to follow from deformed Heisenberg algebras associated with the chiral rings of S_N orbifold CFTs. These deformed algebras are related to quantum groups at roots of unity, and are interpreted as algebras of space-time field creation and annihilation operators. We also propose, as space-time origin of the stringy exclusion principle, that the $ADS_3 \times S^3$ space-time of the associated six-dimensional supergravity theory acquires, when quantum effects are taken into account, a non-commutative structure given by $SU_q(1,1) \times SU_q (2)$. Both remarks imply that finite N effects are captured by quantum groups $SL_q(2)$ with $q= e^{{i \pi \over {N + 1}}}$. This implies that a proper framework for the theories in question is given by gravity on a non-commutative spacetime with a q-deformation of field oscillators. An interesting consequence of this framework is a holographic interpretation for a product structure in the space of all unitary representations of the non-compact quantum group $SU_q(1,1)$ at roots of unity.Comment: 28 pages in harvmac big ; v2: Minor corrections, ref adde