Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userColor-dressed string disk amplitudes and the descent algebra
69
0
0.0
(
0
)
Authors
Carlos R. Mafra
Ask ChatGPT about the research
No Arabic abstract
Inspired by the definition of color-dressed amplitudes in string theory, we define analogous color-dressed permutations replacing the color-ordered string amplitudes by their corresponding permutations. Decomposing the color traces into symmetrized traces and structure constants, the color-dressed permutations define BRST-invariant permutations, which we show are elements of the inverse Solomon descent algebra. Comparing both definitions suggests a duality between permutations in the inverse descent algebra and kinematics from the higher $alpha$ sector of string disk amplitudes. We analyze the symmetries of the $alpha$ disk corrections and obtain a new decomposition for them, leading to their dimensions given by sums of Stirling cycle numbers. The descent algebra also leads to the interpretation that the ${alpha}^2zeta_2$ correction is orthogonal to the field-theory amplitudes as well as their respective tails of BCJ-preserving interactions. In addition, we show how the superfield expansion of BRST invariants of the pure spinor formalism corresponding to ${alpha}^2$ corrections are encoded in the descent algebra.
rate research
Read More
We study string scattering amplitudes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. The four-string scattering amplitudes with three tachyons and an arbitrary string state are calculated. The string field theory yields the string scattering amplitudes evaluated on the world sheet of string scattering whereas the coventional method, based on the first quantized theory brings us the string scattering amplitudes defined on the upper half plane. For the highest spin states, generated by the primary operators, both calculations are in perfect agreement. In this case, the string scattering amplitudes are invariant under the conformal transformation, which maps the string world sheet onto the upper half plane. If the external string states are general massive states, generated by non-primary field operators, we need to take into account carefully the conformal transformation between the world sheet and the upper half plane. We show by an explicit calculation that the string scattering amplitudes calculated by using the deformed cubic string field theory transform into those of the first quantized theory on the upper half plane by the conformal transformation, generated by the Schwarz-Christoffel mapping.
It is shown that the generating function of $mathscr{N}=2$ topological strings, in the heterotic weak coupling limit, is identified with the partition function of a six-dimensional Melvin background. This background, which corresponds to an exact CFT, realises in string theory the six-dimensional $varOmega$-background of Nekrasov, in the case of opposite deformation parameters $epsilon_1=-epsilon_2$, thus providing the known perturbative part of the Nekrasov partition function in the field theory limit. The analysis is performed on both heterotic and type I strings and for the cases of ordinary $mathscr{N}=2$ and $mathscr{N}=2^*$ theories.
We obtain classical string solutions on RxS^2 by applying the dressing method on string solutions with elliptic Pohlmeyer counterparts. This is realized through the use of the simplest possible dressing factor, which possesses just a pair of poles lying on the unit circle. The latter is equivalent to the action of a single Backlund transformation on the corresponding sine-Gordon solutions. The obtained dressed elliptic strings present an interesting bifurcation of their qualitative characteristics at a specific value of a modulus of the seed solutions. Finally, an interesting generic feature of the dressed strings, which originates from the form of the simplest dressing factor and not from the specific seed solution, is the fact that they can be considered as drawn by an epicycle of constant radius whose center is running on the seed solution. The radius of the epicycle is directly related to the location of the poles of the dressing factor.
We reproduce the asymptotic expansion of the D1D5 microstate geometries by computing the emission amplitudes of closed string states from disks with mixed D1D5 boundary conditions. Thus we provide a direct link between the supergravity and D-brane descriptions of the D1D5 microstates at non-zero string coupling. Microscopically, the profile functions characterizing the microstate solutions are encoded in the choice of a condensate for the twisted open string states connecting D1 and D5 branes.
The sum over planar multi-loop diagrams in the NS+ sector of type 0 open strings in flat spacetime has been proposed by Thorn as a candidate to resolve non-perturbative issues of gauge theories in the large $N$ limit. With $SU (N)$ Chan-Paton factors, the sum over planar open string multi-loop diagrams describes the t Hooft limit $Nto infty$ with $Ng_s^2$ held fixed. By including only planar diagrams in the sum the usual mechanism for the cancellation of loop divergences (which occurs, for example, among the planar and Mobius strip diagrams by choosing a specific gauge group) is not available and a renormalization procedure is needed. In this article the renormalization is achieved by suspending total momentum conservation by an amount $pequiv sum_i^n k_i eq 0$ at the level of the integrands in the integrals over the moduli and analytically continuing them to $p=0$ at the very end. This procedure has been successfully tested for the 2 and 3 gluon planar loop amplitudes by Thorn. Gauge invariance is respected and the correct running of the coupling in the limiting gauge field theory was also correctly obtained. In this article we extend those results in two directions. First, we generalize the renormalization method to an arbitrary $n$-gluon planar loop amplitude giving full details for the 4-point case. One of our main results is to provide a fully renormalized amplitude which is free of both UV and the usual spurious divergences leaving only the physical singularities in it. Second, using the complete renormalized amplitude, we extract the high-energy scattering regime at fixed angle (tensionless limit). Apart from obtaining the usual exponential falloff at high energies, we compute the full dependence on the scattering angle which shows the existence of a smooth connection between the Regge and hard scattering regimes.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
