9,080 research outputs found
Loop Variables and Gauge Invariance in (Open) Bosonic String Theory
We give a simplified and more complete description of the loop variable
approach for writing down gauge invariant equations of motion for the fields of
the open string. A simple proof of gauge invariance to all orders is given. In
terms of loop variables, the interacting equations look exactly like the free
equations, but with a loop variable depending on an extra parameter, thus
making it a band of finite width. The arguments for gauge invariance work
exactly as in the free case. We show that these equations are Wilsonian RG
equations with a finite world-sheet cutoff and that in the infrared limit,
equivalence with the Callan-Symanzik -functions should ensure that they
reproduce the on-shell scattering amplitudes in string theory. It is applied to
the tachyon-photon system and the general arguments for gauge invariance can be
easily checked to the order calculated. One can see that when there is a finite
world sheet cutoff in place, even the U(1) invariance of the equations for the
photon, involves massive mode contributions. A field redefinition involving the
tachyon is required to get the gauge transformations of the photon into
standard form.Comment: 20 pages, Late
Constraints on Low-Dimensional String Compactifications
We study the restrictions imposed by cancellation of the tadpoles for two,
three, and four-form gauge fields in string theory, M-theory and F-theory
compactified to two, three and four dimensions, respectively. For a large class
of supersymmetric vacua, turning on a sufficient number of strings, membranes
and three-branes, respectively, can cancel the tadpoles, and preserve
supersymmetry. However, there are cases where the tadpole cannot be removed in
this way, either because the tadpole is fractional, or because of its sign. For
M-theory and F-theory compactifications, we also explore the relation of the
membranes and three-branes to the nonperturbative space-time superpotential.Comment: 16 pages, harvma
Field Theory of Tachyon Matter
We propose a field theory for describing the tachyon on a brane-antibrane
system near the minimum of the potential. This field theory realizes two known
properties of the tachyon effective action: 1) absence of plane-wave solutions
around the minimum, and 2) exponential fall off of the pressure at late time as
the tachyon field evolves from any spatially homogeneous initial configuration
towards the minimum of the potential. Classical solutions in this field theory
include non-relativistic matter with arbitrary spatial distribution of energy.Comment: LaTeX file, 9 pages, discussion of classical solutions expanded,
other minor change
Conformal Field Theory of AdS Background with Ramond-Ramond Flux
We review a formalism of superstring quantization with manifest
six-dimensional spacetime supersymmetry, and apply it to AdS_3 x S^3
backgrounds with Ramond-Ramond flux. The resulting description is a conformal
field theory based on a sigma model whose target space is a certain supergroup
SU'(2|2).Comment: 89 pages harvmac. Added four reference
Spinning flavour branes and fermion pairing instabilities
We consider probe Dp-branes, p=3,5,7, in global AdS_5 x S^5, rotating along
an internal direction in the S^5. These are dual to strongly interacting N=4
SYM on S^3 with massless fundamental flavours, in the presence of an R-symmetry
chemical potential for flavour fermions. For massless, "AdS-filling" Dp-brane
embeddings at zero temperature, we find an infinite set of threshold values of
the chemical potential at which instabilities are triggered. The onset of
instability is always preceded by metastability of the zero density state. From
the onset values of the chemical potential, we infer that unstable directions
favour a homogeneous condensate of a bilinear made from fermion harmonics, or
Cooper pairing. We confirm this picture both numerically and analytically. The
linearized analysis showing the appearance of instabilities involves a charged
scalar in global AdS space coupled to a (large) constant background gauge
potential. The resulting frequency space correlator of the fermion bilinear at
strong coupling displays poles in the upper half plane. In contrast, the
correlator at zero coupling exhibits Pauli blocking due to occupation of states
below the Fermi level, but no instabilities. The end-point of the strong
coupling instability is not visible in our setup.Comment: 44 pages, 10 figures, uses late
Topological Reduction of 4D SYM to 2D --Models
By considering a (partial) topological twisting of supersymmetric Yang-Mills
compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a
supersymmetric -model in 2 dimensions. For N=2 SYM this maps Donaldson
observables on products of two Riemann surfaces to quantum cohomology ring of
moduli space of flat connections on a Riemann surface. For N=4 SYM it maps
-duality to -duality for -models on moduli space of solutions to
Hitchin equations.Comment: 30 pages, harvma
A remark on the matrix Airy function
An integral representation for matrix Airy function is presentedComment: 4 page
Perspectives on Pfaffians of Heterotic World-sheet Instantons
To fix the bundle moduli of a heterotic compactification one has to
understand the Pfaffian one-loop prefactor of the classical instanton
contribution. For compactifications on elliptically fibered Calabi-Yau spaces X
this can be made explicit for spectral bundles and world-sheet instantons
supported on rational base curves b: one can express the Pfaffian in a closed
algebraic form as a polynomial, or it may be understood as a theta-function
expression. We elucidate the connection between these two points of view via
the respective perception of the relevant spectral curve, related to its
extrinsic geometry in the ambient space (the elliptic surface in X over b) or
to its intrinsic geometry as abstract Riemann surface. We identify, within a
conceptual description, general vanishing loci of the Pfaffian, and derive
bounds on the vanishing order, relevant to solutions of W=dW=0.Comment: 40 pages; minor changes, discussion section 1.1 adde
Di-Jet Conical Correlations Associated with Heavy Quark Jets in anti--de Sitter Space/Conformal Field Theory Correspondence
We show that far zone Mach and diffusion wake ``holograms'' produced by
supersonic strings in anti--de Sitter space/conformal field theory (AdS/CFT)
correspondence do not lead to observable conical angular correlations in the
strict supergravity limit if Cooper-Frye hadronization is
assumed. However, a special {\em nonequilibrium} ``neck'' zone near the jet is
shown to produce an apparent sonic boom azimuthal angle distribution that is
roughly independent of the heavy quark's velocity. Our results indicate that a
measurement of the dependence of the away-side correlations on the velocity of
associated identified heavy quark jets at the BNL Relativistic Heavy Ion
Collider and CERN LHC will provide a direct test of the nonperturbative
dynamics involved in the coupling between jets and the strongly-coupled
Quark-Gluon Plasma (sQGP) implied by AdS/CFT correspondence.Comment: 4 pages, 2 figures, version published in Physical Review Letter
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