Browsing by Author "Pinzul, A."

Now showing 1 - 6 of 6
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    Absence of the Holographic Principle in Noncommutative Chern-Simons Theory
    (2001-12-03) Pinzul, A.; Stern, Allen; University of Alabama Tuscaloosa
    We examine noncommutative Chern-Simons theory on a bounded spatial domain. We argue that upon `turning on' the noncommutativity, the edge observables, which characterized the commutative theory, move into the bulk. We show this to lowest order in the noncommutativity parameter appearing in the Moyal star product. If one includes all orders, the hamiltonian formulation of the gauge theory ceases to exist, indicating that the Moyal star product must be modified in the presence of a boundary. Alternative descriptions are matrix models. We examine one such model, obtained by a simple truncation of Chern-Simons theory on the noncommutative plane, and express its observables in terms of Wilson lines.
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    Dirac Operator on the Quantum Sphere
    (Elsevier, 2001-07-12) Pinzul, A.; Stern, Allen; University of Alabama Tuscaloosa
    We construct a Dirac operator on the quantum sphere S2q which is covariant under the action of SUq(2), compatible with a chirality operator, has the correct commutative limit and also a familiar fuzzy sphere limit. In the fuzzy sphere limit it reduces to Watamuras' Dirac operator. We argue that our Dirac operator may be useful in constructing SUq(2) invariant field theories on S2q following the Connes–Lott approach to noncommutative geometry.
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    Gauge Theory of the Star Product
    (2007-09-25) Pinzul, A.; Stern, Allen; University of Alabama Tuscaloosa
    The choice of a star product realization for non-commutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as integration measures and covariant derivatives on this space. The covariant derivative can be expressed in terms of connections in the usual way giving rise to new degrees of freedom for non-commutative theories.
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    Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere
    (Elsevier, 2001-04-30) Alexanian, G.; Pinzul, A.; Stern, Allen; University of Alabama Tuscaloosa
    We construct a star product associated with an arbitrary two-dimensional Poisson structure using generalized coherent states on the complex plane. From our approach one easily recovers the star product for the fuzzy torus, and also one for the fuzzy sphere. For the latter we need to define the ‘fuzzy’ stereographic projection to the plane and the fuzzy sphere integration measure, which in the commutative limit reduce to the usual formulae for the sphere.
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    A New Class of Two-Dimensional Noncommutative Spaces
    (2002-04-04) Pinzul, A.; Stern, Allen; University of Alabama Tuscaloosa
    We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent states we are able to take the continuum limit, where we recover the punctured plane with non constant Poisson structures.
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    Noncommutative AdS(2)/CFT1 duality: The case of massless scalar fields
    (American Physical Society, 2017-09-18) Pinzul, A.; Stern, A.; Universidade de Brasilia; University of Alabama Tuscaloosa
    We show how to construct correlators for the CFT1 which is dual to noncommutative AdS(2) (ncAdS(2)). We do it explicitly for the example of the massless scalar field on Euclidean ncAdS(2). ncAdS(2) is the quantization of AdS(2) that preserves all the isometries. It is described in terms of the unitary irreducible representations, more specifically discrete series representations, of so(2, 1). We write down symmetric differential representations for the discrete series and then map them to functions on the Moyal-Weyl plane. The Moyal-Weyl plane has a large distance limit which can be identified with the boundary of ncAdS(2). Killing vectors can be constructed on ncAdS(2) which reduce to the AdS(2) Killing vectors near the boundary. We, therefore, conclude that ncAdS(2) is asymptotically AdS(2), and so the AdS/CFT correspondence should apply. For the example of the massless scalar field on Euclidean ncAdS(2), the on-shell action, and resulting two-point function for the boundary theory, are computed to leading order in the noncommutativity parameter. The computation is nontrivial because nonlocal interactions appear in the Moyal-Weyl description. Nevertheless, the result is remarkably simple and agrees with that of the commutative scalar field theory, up to a rescaling.