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Pei-Ming Ho

Publications and source records attributed to Pei-Ming Ho.

At least 109 records · Page 6Linked to original sources
arXiv2000

Fuzzy Spheres in AdS/CFT Correspondence and Holography from Noncommutativity

We show that the existent fuzzy S^2 and S^4 models are natural candidates for the quantum geometry on the corresponding spheres in AdS/CFT correspondence. These models fit nicely the data from the dipole mechanism for the stringy exclusion principle. In the AdS_2 X S^2 case, we show that a wrapped fractional membrane can be used to count for the large ground state degeneracy. We also propose a fuzzy AdS_2 model whose fundamental commutation relation may underlie the UV/IR connection.

hep-th↗
arXiv2000

Twisted Bundle on Noncommutative Space and U(1) Instanton

We study the notion of twisted bundles on noncommutative space. Due to the existence of projective operators in the algebra of functions on the noncommutative space, there are twisted bundles with non-constant dimension. The U(1) instanton solution of Nekrasov and Schwarz is such an example. As a mathematical motivation for not excluding such bundles, we find gauge transformations by which a bundle with constant dimension can be equivalent to a bundle with non-constant dimension.

hep-th↗
arXiv1999

Matrix Theory in a Constant C Field Background

D0-branes moving in a constant antisymmetric C field are found to be described by quantum mechanics of the supersymmetric matrix model with a similarity transformation. Sometimes this similarity transformation is singular or ill-defined and cannot be ignored. As an example, when there are non-vanishing C_{-ij} components, we obtain the theory for Dp-branes which is effectively the noncommutative super Yang-Mills theory. We also briefly discuss the effects of other non-vanishing components such as C_{+ij} and C_{ijk}.

hep-th↗
arXiv1999

Worldvolume Uncertainty Relations for D-Branes

By quantizing an open string ending on a D-brane in a nontrivial supergravity background, we argue that there is a new kind of uncertainty relation on a D-brane worldvolume. Furthermore, we fix the form of the uncertainty relations and their dependence on the string coupling constant by requiring them to be consistent with various string theory and M theory dualities. In this way we find a web of uncertainties of spacetime for all kinds of brane probes, including fundamental strings, D-branes of all dimensions as well as M theory membranes and fivebranes.

hep-th↗
arXiv1999

Quantum Spacetimes and Finite N Effects in 4D Super Yang-Mills Theories

The truncation in the number of single-trace chiral primary operators of $\N=4$ SYM and its conjectured connection with gravity on quantum spacetimes are elaborated. The model of quantum spacetime we use is $AdS^5_q \times S^5_q$ for $q$ a root of unity. The quantum sphere is defined as a homogeneous space with manifest $SU_q(3)$ symmetry, but as anticipated from the field theory correspondence, we show that there is a hidden $SO_q(6)$ symmetry in the constrution. We also study some properties of quantum space quotients as candidate models for the quantum spacetime relevant for some $Z_n$ quiver quotients of the $\N=4$ theory which break SUSY to $\N=2$. We find various qualitative agreements between the proposed models and the properties of the corresponding finite $N$ gauge theories.

hep-th↗
arXiv1999

Noncommutative Open String and D-brane

In this paper we consider the quantization of open strings ending on D-branes with a background B field. We find that spacetime coordinates of the open string end-points become noncommutative, and correspondingly the D-brane worldvolume also becomes noncommutative. This provides a string theory derivation and generalization of the noncommutativity obtained previously in the Matrix model compactification. For Dp-branes with p>=2 our results are new and agree with that of Matrix theory for the case of A=0 (where $A$ is the worldvolume gauge field) if the T-duality radii are used.

hep-th↗
arXiv1998

Matrix Compactification On Orientifolds

Generalizing previous results for orbifolds, in this paper we describe the compactification of Matrix model on an orientifold which is a quotient space as a Yang-Mills theory living on a quantum space. The information of the compactification is encoded in the action of the discrete symmetry group G on Euclidean space and a projective representation U of G. The choice of Hilbert space on which the algebra of U is realized as an operator algebra corresponds to the choice of a physical background for the compactification. All these data are summarized in the spectral triple of the quantum space.

hep-th↗
arXiv1998

D-Instanton in AdS_5 and Instanton in SYM_4

Following the observation of Banks and Green that the D-instantons in AdS_5 correspond to the instantons in 4-dimensional supersymmetric Yang-Mills theory, we study in more detail this correspondence for individual instantons. The supergravity solution for a D-instanton in AdS_5 is found using the ansatz used previously for D-instantons in flat space. We check that the actions and supersymmetries match between the D-instanton solution and the Yang-Mills instanton. Generalizing this result, we propose that any supergravity solution satisfying the ansatz corresponds to a (anti-)self-dual Yang-Mills configuration. Using this ansatz a family of identities for correlation functions in the supersymmetric Yang-Mills theory are derived.

hep-th↗
arXiv1998

Noncommutative Gauge Theories in Matrix Theory

We present a general framework for Matrix theory compactified on a quotient space R^n/G, with G a discrete group of Euclidean motions in R^n. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We characterize the resulting noncommutative gauge theory in terms of the twisted group algebra of G associated with a projective regular representation. Also we show how to extend our treatments to incorporate orientifolds.

hep-th↗
arXiv1998

Twisted Bundle On Quantum Torus and BPS States in Matrix Theory

Following the recent work of Connes, Douglas and Schwarz, we study the M(atrix) model compactified on a torus with a background of the three-form field. This model is given by a super Yang-Mills theory on a quantum torus. To consider twisted gauge field configurations, we construct twisted U(n) bundles on the quantum torus as a deformation of its classical counterpart. By properly taking into account membranes winding around the light-cone direction, we derive from the M(atrix) model the BPS spectrum which respects the full SL(2,Z)*SL(2,Z) U-duality in M theory.

hep-th↗
arXiv1998

Towards a Noncommutative Geometric Approach to Matrix Compactification

In this paper we study generic M(atrix) theory compactifications that are specified by a set of quotient conditions. A procedure is proposed, which both associates an algebra to each compactification and leads deductively to general solutions for the matrix variables. The notion of noncommutative geometry on the dual space is central to this construction. As examples we apply this procedure to various orbifolds and orientifolds, including ALE spaces and quotients of tori. While the old solutions are derived in a uniform way, new solutions are obtained in several cases. Our study also leads to a new formulation of gauge theory on quantum spaces.

hep-th↗
arXiv1997

Brane Creation in M(atrix) Theory

We discuss, in the context of M(atrix) theory, the creation of a membrane suspendend between two longitudinal five-branes when they cross each other. It is shown that the membrane creation is closely related to the degrees of freedom in the off-diagonal blocks which are related via dualities to the chiral fermionic zero mode on a 0-8 string. In the dual system of a D0-brane and a D8-brane in type \IIA theory the half-integral charges associated with the ``half''-strings are found to be connected to the well-known fermion-number fractionalization in the presence of a fermionic zero mode. At sufficiently short distances, the effective potential between the two five-branes is dominated by the zero mode contribution to the vacuum energy.

hep-th↗
arXiv1997

P-P' Strings in M(atrix) Theory

We study the off-diagonal blocks in the M(atrix) model that are supposed to correspond to open strings stretched between a Dp-brane and a Dp'-brane. It is shown that the spectrum, including the quantum numbers, of the zero modes in the off-diagonal blocks can be determined from the index theorem and unbroken supersymmetry, and indeed reproduces string theory predictions for p-p' strings. Previously the matrix description of a longitudinal fivebrane needed to introduce extra degrees of freedom corresponding to 0-4 strings by hand. We show that they are naturally associated with the off-diagonal zero modes, and the supersymmetry transformation laws and low energy effective action postulated for them are now derivable from the M(atrix) theory.

hep-th↗
arXiv1997

IIB/M Duality and Longitudinal Membranes in M(atrix) Theory

In this paper we study duality properties of the M(atrix) theory compactified on a circle. We establish the equivalence of this theory to the strong coupling limit of type IIB string theory compactified on a circle. In the M(atrix) theory context, our major evidence for this duality consists of identifying the BPS states of IIB strings in the spectrum and finding the remnant symmetry of SL(2,Z) and the associated tau moduli. By this IIB/M duality, a number of insights are gained into the physics of longitudinal membranes in the infinite momentum frame. We also point out an accidental affine Lie symmetry in the theory.

hep-th↗
arXiv1997

Poisson Algebra of Differential Forms

We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on differential calculus in a simple canonical form by a coordinate transformation. This is in analogy with the standard Darboux's theorem for symplectic geometry. For certain cases there exists a realization of the exterior derivative through a certain canonical one-form. All the above are carried out similarly for the case of a complex Poisson Differential Algebra. The case of one complex dimension is treated in details and interesting features are noted. A conclusion is made in the last section.

q-alg↗
arXiv1996

Noncommutative Geometry and D-Branes

We apply noncommutative geometry to a system of N parallel D-branes, which is interpreted as a quantum space. The Dirac operator defining the quantum differential calculus is identified to be the supercharge for strings connecting D-branes. As a result of the calculus, Connes' Yang-Mills action functional on the quantum space reproduces the dimensionally reduced U(N) super Yang-Mills action as the low energy effective action for D-brane dynamics. Several features that may look ad hoc in a noncommutative geometric construction are shown to have very natural physical or geometric origin in the D-brane picture in superstring theory.

hep-th↗
arXiv1996

Some Complex Quantum Manifolds and their Geometry

After recalling briefly some basic properties of the quantum group $GL_q(2)$, we study the quantum sphere $S_q^2$, quantum projective space $CP_q(N)$ and quantum Grassmannians as examples of complex (Kähler) quantum manifolds. The differential and integral calculus on these manifolds are discussed. It is shown that many relations of classical projective geometry generalize to the quantum case. For the case of the quantum sphere a comparison is made with A. Connes' method.

hep-th↗