2,503 research outputs found
Relativistic field theories in a magnetic background as noncommutative field theories
We study the connection of the dynamics in relativistic field theories in a
strong magnetic field with the dynamics of noncommutative field theories
(NCFT). As an example, the Nambu-Jona-Lasinio models in spatial dimensions are considered. We show that this connection is rather sophisticated.
In fact, the corresponding NCFT are different from the conventional ones
considered in the literature. In particular, the UV/IR mixing is absent in
these theories. The reason of that is an inner structure (i.e., dynamical
form-factors) of neutral composites which plays an important role in providing
consistency of the NCFT. An especially interesting case is that for a magnetic
field configuration with the maximal number of independent nonzero tensor
components. In that case, we show that the NCFT are finite for even and
their dynamics is quasi-(1+1)-dimensional for odd . For even , the NCFT
describe a confinement dynamics of charged particles. The difference between
the dynamics in strong magnetic backgrounds in field theories and that in
string theories is briefly discussed.Comment: 19 pages, REVTeX4, clarifications added, references added, to appear
in Phys. Rev.
The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized
at the one-loop level by multiplicative dimensional renormalization of the
coupling constant and fields of the theory. We compute the beta function of the
theory and conclude that the theory is asymptotically free. We also show that
the Weyl-Moyal matrix defining the deformed product over the space of functions
on R^4 is not renormalized at the one-loop level.Comment: 8 pages. A missing complex "i" is included in the field strength and
the divergent contributions corrected accordingly. As a result the model
turns out to be asymptotically fre
Effective Finite Temperature Partition Function for Fields on Non-Commutative Flat Manifolds
The first quantum correction to the finite temperature partition function for
a self-interacting massless scalar field on a dimensional flat manifold
with non-commutative extra dimensions is evaluated by means of dimensional
regularization, suplemented with zeta-function techniques. It is found that the
zeta function associated with the effective one-loop operator may be nonregular
at the origin. The important issue of the determination of the regularized
vacuum energy, namely the first quantum correction to the energy in such case
is discussed.Comment: amslatex, 14 pages, to appear in Phys. Rev.
Orientifolds of Matrix theory and Noncommutative Geometry
We study explicit solutions for orientifolds of Matrix theory compactified on
noncommutative torus. As quotients of torus, cylinder, Klein bottle and
M\"obius strip are applicable as orientifolds. We calculate the solutions using
Connes, Douglas and Schwarz's projective module solution, and investigate
twisted gauge bundle on quotient spaces as well. They are Yang-Mills theory on
noncommutative torus with proper boundary conditions which define the geometry
of the dual space.Comment: 17 pages, LaTeX, minor corrections, two references added, discussions
slightly expanded, to appear in Phys. Rev.
Topological Orthoalgebras
We define topological orthoalgebras (TOAs) and study their properties. While
every topological orthomodular lattice is a TOA, the lattice of projections of
a Hilbert space is an example of a lattice-ordered TOA that is not a toplogical
lattice. On the other hand, we show that every compact Boolean TOA is a
topological Boolean algebra. We also show that a compact TOA in which 0 is an
isolated point is atomic and of finite height. We identify and study a
particularly tractable class of TOAs, which we call {\em stably ordered}: those
in which the upper-set generated by an open set is open. This includes all
topological OMLs, and also the projection lattices of Hilbert spaces. Finally,
we obtain a topological version of the Foulis-Randall representation theory for
stably ordered TOAsComment: 16 pp, LaTex. Minor changes and corrections in sections 1; more
substantial corrections in section
Canonical Quantization of Open String and Noncommutative Geometry
We perform canonical quantization of open strings in the -brane background
with a -field. Treating the mixed boundary condition as a primary
constraint, we get a set of secondary constraints. Then these constraints are
shown to be equivalent to orbifold conditions to be imposed on normal string
modes. These orbifold conditions are a generalization of the familiar orbifold
conditions which arise when we describe open strings in terms of closed
strings. Solving the constraints explicitly, we obtain a simple Hamiltonian for
the open string, which reveals the nature of noncommutativity transparently.Comment: 14 pages, RevTex, added reference
Noncommutative geometry and physics: a review of selected recent results
This review is based on two lectures given at the 2000 TMR school in Torino.
We discuss two main themes: i) Moyal-type deformations of gauge theories, as
emerging from M-theory and open string theories, and ii) the noncommutative
geometry of finite groups, with the explicit example of Z_2, and its
application to Kaluza-Klein gauge theories on discrete internal spaces.Comment: Based on lectures given at the TMR School on contemporary string
theory and brane physics, Jan 26- Feb 2, 2000, Torino, Italy. To be published
in Class. Quant. Grav. 17 (2000). 3 ref.s added, typos corrected, formula on
exterior product of n left-invariant one-forms corrected, small changes in
the Sect. on integratio
Twisted Bundles on Noncommutative and D-brane Bound States
We construct twisted quantum bundles and adjoint sections on noncommutative
, and investigate relevant D-brane bound states with non-Abelian
backgrounds. We also show that the noncommutative with non-Abelian
backgrounds exhibits SO duality and via this duality we get a Morita
equivalent on which only D0-branes exist. For a reducible non-Abelian
background, the moduli space of D-brane bound states in Type II string theory
takes the form .Comment: 19 pages, Latex. v2: Title is changed. Minor corrections. A reference
adde
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.Comment: 19 pages, minor modification on p.
The Entropy of 4D Black Holes and the Enhancon
We consider the physics of enhancons as applied to four dimensional black
holes which are constructed by wrapping both D-branes and NS-branes on K3. As
was recently shown for the five dimensional black holes, the enhancon is
crucial in maintaining consistency with the second law of thermodynamics. This
is true for both the D-brane and NS-brane sectors of these black holes. In
particular NS5-branes in both type IIA and IIB string theory are found to
exhibit enhancon physics when wrapped on a K3 manifold.Comment: 23 pages. 1 figure. Minor typos corrected. Refs added. To appear in
PR
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