373 research outputs found

### Seiberg-Witten Curve for the E-String Theory

We construct the Seiberg-Witten curve for the E-string theory in
six-dimensions. The curve is expressed in terms of affine E_8 characters up to
level 6 and is determined by using the mirror-type transformation so that it
reproduces the number of holomorphic curves in the Calabi-Yau manifold and the
amplitudes of N=4 U(n) Yang-Mills theory on 1/2 K3. We also show that our curve
flows to known five- and four-dimensional Seiberg-Witten curves in suitable
limits.Comment: 18 pages, 1 figure; appendix C adde

### Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons

Both in string field theory and in p-adic string theory the equations of
motion involve infinite number of time derivatives. We argue that the initial
value problem is qualitatively different from that obtained in the limit of
many time derivatives in that the space of initial conditions becomes strongly
constrained. We calculate the energy-momentum tensor and study in detail time
dependent solutions representing tachyons rolling on the p-adic string theory
potentials. For even potentials we find surprising small oscillations at the
tachyon vacuum. These are not conventional physical states but rather
anharmonic oscillations with a nontrivial frequency--amplitude relation. When
the potentials are not even, small oscillatory solutions around the bottom must
grow in amplitude without a bound. Open string field theory resembles this
latter case, the tachyon rolls to the bottom and ever growing oscillations
ensue. We discuss the significance of these results for the issues of emerging
closed strings and tachyon matter.Comment: 46 pages, 14 figures, LaTeX. Replaced version: Minor typos corrected,
some figures edited for clarit

### Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories

In arXiv:0908.2463 we computed the four-loop correction to a function
depending on the 't Hooft coupling(s) that appears in the magnon dispersion
relation of the spin chains derived from single trace operators in N=6
superconformal Chern-Simons theories. In this paper we give detailed
descriptions of this calculation and the computation of the four-loop wrapping
corrections for a length four operator in the 20 of SU(4), the R-symmetry group
for these theories. Here, we give all relevant Feynman diagrams and loop
integrals explicitly, and also demonstrate the cancellation of double poles in
the logarithm of the renormalization constant.Comment: LaTeX, feynmp, 70 pages; v2: signs of three diagrams due to
inconsistent Feynman rules corrected, modifying the final result, typos
corrected, formulations improve

### Instanton Expansions for Mass Deformed N=4 Super Yang-Mills Theories

We derive modular anomaly equations from the Seiberg-Witten-Donagi curves for
softly broken N=4 SU(n) gauge theories. From these equations we can derive
recursion relations for the pre-potential in powers of m^2, where m is the mass
of the adjoint hypermultiplet. Given the perturbative contribution of the
pre-potential and the presence of ``gaps'' we can easily generate the m^2
expansion in terms of polynomials of Eisenstein series, at least for relatively
low rank groups. This enables us to determine efficiently the instanton
expansion up to fairly high order for these gauge groups, e. g. eighth order
for SU(3). We find that after taking a derivative, the instanton expansion of
the pre-potential has integer coefficients. We also postulate the form of the
modular anomaly equations, the recursion relations and the form of the
instanton expansions for the SO(2n) and E_n gauge groups, even though the
corresponding Seiberg-Witten-Donagi curves are unknown at this time.Comment: harvmac(b) 28 page

### Quasilocality of joining/splitting strings from coherent states

Using the coherent state formalism we calculate matrix elements of the
one-loop non-planar dilatation operator of ${\cal N}=4$ SYM between operators
dual to folded Frolov-Tseytlin strings and observe a curious scaling behavior.
We comment on the {\it qualitative} similarity of our matrix elements to the
interaction vertex of a string field theory. In addition, we present a solvable
toy model for string splitting and joining. The scaling behaviour of the matrix
elements suggests that the contribution to the genus one energy shift coming
from semi-classical string splitting and joining is small.Comment: 17 pages, 7 figures in 11 file

### Tachyon Dynamics and the Effective Action Approximation

Recently effective actions have been extensively used to describe tachyon
condensation in string theory. While the various effective actions which have
appeared in the literature have very similar properties for static
configurations, they differ for time-dependent tachyons. In this paper we
discuss general properties of non-linear effective Lagrangians which are first
order in derivatives. In particular we show that some observed properties, such
as asymptotically vanishing pressure, are rather generic features, although the
quantative features differ. On the other hand we argue that certain features of
marginal tachyon profiles are beyond the reach of any first order Lagrangian
description. We also point out that an effective action, proposed earlier,
captures the dynamics of tachyons well.Comment: References added and confusing reference clarifie

### Realization of Brane Descent Relations in Effective Theories

We examine Sen's descent relations among (non-)BPS D-branes by using low
energy effective field theories of DpDpbar system. We find that the fluctuation
around the kink solution reproduces the low energy matter content on a non-BPS
D(p-1)-brane. The effective action for these fluctuation modes turns out to be
a generalization of Minahan-Zwiebach model. In addition, it is shown that the
fluctuations around the vortex solution consist of massless fields on a BPS
D(p-2)-brane and they are subject to Dirac-Born-Infeld action. We find the
universality that the above results do not refer to particular forms of the
effective action.Comment: 24 pages, LaTeX, 1 eps figure; v2:minor correction

### Brane Decay and Death of Open Strings

We show how open strings cease to propagate when unstable D-branes decay. The
information on the propagation is encoded in BSFT two-point functions for
arbitrary profiles of open string excitations. We evaluate them in tachyon
condensation backgrounds corresponding to (i) static spatial tachyon kink (=
lower dimensional BPS D-brane) and (ii) homogeneous rolling tachyon. For (i)
the propagation is restricted to the directions along the tachyon kink, while
for (ii) all the open string excitations cease to propagate at late time and
are subject to a collapsed light cone characterized by Carrollian contraction
of Lorentz group.Comment: 19 pages, published version (typos corrected, a reference added

### Plane wave limit of local conserved charges

We study the plane wave limit of the Backlund transformations for the
classical string in AdS space times a sphere and obtain an explicit expression
for the local conserved charges. We show that the Pohlmeyer charges become in
the plane wave limit the local integrals of motion of the free massive field.
This fixes the coefficients in the expansion of the anomalous dimension as the
sum of the Pohlmeyer charges.Comment: v2: added explanation

### Effective theory for wall-antiwall system

We propose a useful method for deriving the effective theory for a system
where BPS and anti-BPS domain walls coexist. Our method respects an
approximately preserved SUSY near each wall. Due to the finite width of the
walls, SUSY breaking terms arise at tree-level, which are exponentially
suppressed. A practical approximation using the BPS wall solutions is also
discussed. We show that a tachyonic mode appears in the matter sector if the
corresponding mode function has a broader profile than the wall width.Comment: LaTeX file, 30 page, 5 eps figures, references adde

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