FINITE Q-OSCILLATOR REPRESENTATION OF 2-<font>D</font> STRING THEORY

Jevicki, Antal; Tonder, André van

doi:10.1142/s0217732396001405

Cited by 16 publications

(19 citation statements)

References 11 publications

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“…Using the match of KK states with generating chiral primaries [7], the cutoff on such chiral primaries in the CFT was analyzed and shown to be in agreement with the above SU q (2) × SU q (1, 1) spacetime. Another way to arrive at the same value of q was dynamical as in similar work in earlier matrix models [8]. An SL q (2) subalgebra was identified in the algebra generated by the chiral primaries and their conjugates.…”

Section: Introductionmentioning

confidence: 94%

Gravity from CFT on S(X) : symmetries and interactions

Jevicki¹,

Mihailescu²,

Ramgoolam³

2000

Nuclear Physics B

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116

179

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The orbifold CFT dual to string theory on ADS 3 ×S 3 allows a construction of gravitational actions based on collective field techniques. We describe a fundamental role played by a Lie algebra constructed from chiral primaries and their CFT conjugates. The leading terms in the algebra at large N are derived from the computation of chiral primary correlation functions. The algebra is argued to determine the dynamics of the theory, its representations provide free and interacting hamiltonians for chiral primaries. This dynamics is seen to be given by an effective one plus one dimensional field theory. The structure of the algebra and its representations shows qualitatively new features associated with thresholds at L 0 = N , L 0 = N/2 and L 0 = N/4, which are related to the stringy exclusion principle and to black holes. We observe relations between fusion rules of SU q (2|1, 1) for q = e iπ N +1 , and the correlation functions, which provide further evidence for a non-commutative spacetime. 11/98

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Section: Introductionmentioning

confidence: 94%

Gravity from CFT on S(X) : symmetries and interactions

Jevicki¹,

Mihailescu²,

Ramgoolam³

2000

Nuclear Physics B

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116

179

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“…The connection between Symmetric and Unitary groups was crucial in the development of the String theory of two-dimensional Yang Mills Theory [17,18,19,20,21,22,23,24] and in certain aspects of Low-dimensional Matrix Models [25,26]. Some key useful results are collected here.…”

mentioning

confidence: 99%

Exact correlators of giant gravitons from dual $N = 4$ SYM theory

Corley

Jevicki²,

Ramgoolam³

2001

Advances in Theoretical and Mathematical Physics

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515

1,226

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A class of correlation functions of half-BPS composite operators are computed exactly ( at finite JV ) in the zero coupling limit of iV = 4 SYM theory. These have a simple dependence on the fourdimensional spacetime coordinates and are related to correlators in a one-dimensional Matrix Model with complex Matrices obtained by dimensional reduction of iV = 4 SYM on a three-sphere. A key technical tool is Frobenius-Schur duality between symmetric and Unitary groups and the results are expressed simply in terms of U(N) group integrals or equivalently in terms of Littlewood-Richardson coefficients. These correlation functions are used to understand the existence/properties of giant gravitons and related solutions in the string theory dual on AdSs x 5 5 . Some of their properties hint at integrability in N = 4 SYM.

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“…Then we can restrict the algebra by a † a = φ(N)θ(N), where θ(N) is 0 or 1, depending on whether the given N -particle (excitation) state is forbidden or allowed. The simplest case [22] is θ(n) = 1, n ≤ p and θ(n) = 0, n > p.…”

Section: Restricted Algebras and Projected Fock Spacesmentioning

confidence: 99%

“…Generally, the Gentile-type statistics can be defined by As example, we consider restricted Bose oscillator 5) with Fock space spanned by |0 >, a † |0 >, ...(a † ) m |0 >. This oscillator coincides with the truncated Bose oscillator with cutoff [22] aa † = (1 + a † a) − (N + 1) δ N,m (4.6) or aa † = Θ(m − N + 1). The counting rule is…”

Section: Gentile -Type Statistics : Restrictions On Each Single Oscilmentioning

confidence: 99%

Exclusion statistics, operator algebras and Fock space representations

Meljanac

Mileković²,

Stojić

1999

J. Phys. A: Math. Gen.

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We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio. We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space , where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys. Lett.A 11, 3081 (1996) AbstractWe study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio. We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space , where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys. Lett.A 11, 3081 (1996), and associated counting rules. Within these three types of exclusions in Fock space the original Haldane exclusion statistics cannot be realized.3

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FINITE Q-OSCILLATOR REPRESENTATION OF 2-D STRING THEORY

Cited by 16 publications

References 11 publications

Gravity from CFT on S(X) : symmetries and interactions

Gravity from CFT on S(X) : symmetries and interactions

Exact correlators of giant gravitons from dual $N = 4$ SYM theory

Exclusion statistics, operator algebras and Fock space representations

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