71 research outputs found
Soft behavior of string amplitudes with external massive states
We briefly discuss the soft behavior of scattering amplitudes both in string
and quantum field theory. In particular we show a general argument about the
validity of soft theorems for open superstring amplitudes and list some of our
recent results.Comment: 2 pages, poster presented at IFAE 201
On the soft limit of closed string amplitudes with massive states
We extend our analysis of the soft behaviour of string amplitudes with
massive insertions to closed strings at tree level (sphere). Relying on our
previous results for open strings on the disk and on KLT formulae we check
universality of the soft behaviour for gravitons to sub-leading order for
superstring amplitudes and show how this gets modified for bosonic strings. At
sub-sub-leading order we argue in favour of universality for superstrings on
the basis of OPE of the vertex operators and gauge invariance for the soft
graviton. The results are illustrated by explicit examples of 4-point
amplitudes with one massive insertion in any dimension, including D=4, where
use of the helicity spinor formalism drastically simplifies the expressions. As
a by-product of our analysis we confirm that the `single valued projection'
holds for massive amplitudes, too. We briefly comment on the soft behaviour of
the anti-symmetric tensor and on loop corrections.Comment: 18+7 pages; added some important references and corrected some typo
Bootstrapping QCD: the Lake, the Peninsula and the Kink
We consider the S-matrix bootstrap of four dimensional scattering amplitudes
with symmetry and no bound-states. We explore the allowed space of
scattering lengths which parametrize the interaction strength at threshold of
the various scattering channels. Next we consider an application of this
formalism to pion physics. A signature of pions is that they are derivatively
coupled leading to (chiral) zeros in their scattering amplitudes. In this work
we explore the multi-dimensional space of chiral zeros positions, scattering
length values and resonance mass values. Interestingly, we encounter lakes,
peninsulas and kinks depending on which sections of this intricate
multi-dimensional space we consider. We discuss the remarkable location where
QCD seems to lie in these plots, based on various experimental and theoretical
expectations.Comment: 6 pages, 7 figure
On the exactness of soft theorems
Soft behaviours of S-matrix for massless theories reflect the underlying
symmetry principle that enforces its masslessness. As an expansion in soft
momenta, sub-leading soft theorems can arise either due to (I) unique structure
of the fundamental vertex or (II) presence of enhanced broken-symmetries. While
the former is expected to be modified by infrared or ultraviolet divergences,
the latter should remain exact to all orders in perturbation theory. Using
current algebra, we clarify such distinction for spontaneously broken (super)
Poincar\'e and (super) conformal symmetry. We compute the UV divergences of
DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft
theorems, while type (I) are shown to be broken and the soft-modifying
higher-dimensional operators are identified. As further evidence for the
exactness of type (II) soft theorems, we consider the alpha' expansion of both
super and bosonic open strings amplitudes, and verify the validity of the
translation symmetry breaking soft-theorems up to O(alpha'^6). Thus the
massless S-matrix of string theory "knows" about the presence of D-branes.Comment: 35 pages. Additional mathematica note book with the UV-divergenece of
the 6-point amplitude in AV/KS theor
Exploring soft constraints on effective actions
We study effective actions for simultaneous breaking of space-time and
internal symmetries. Novel features arise due to the mixing of Goldstone modes
under the broken symmetries which, in contrast to the usual Adler's zero, leads
to non-vanishing soft limits. Such scenarios are common for spontaneously
broken SCFT's. We explicitly test these soft theorems for sYM
in the Coulomb branch both perturbatively and non-perturbatively. We explore
the soft constraints systematically utilizing recursion relations. In the pure
dilaton sector of a general CFT, we show that all amplitudes up to order are completely determined in terms of the -point
amplitudes at order with . Terms with at most one derivative
acting on each dilaton insertion are completely fixed and coincide with those
appearing in the conformal DBI, i.e. DBI in AdS. With maximal supersymmetry,
the effective actions are further constrained, leading to new
non-renormalization theorems. In particular, the effective action is fixed up
to eight derivatives in terms of just one unknown four-point coefficient and
one more coefficient for ten-derivative terms. Finally, we also study the
interplay between scale and conformal invariance in this context.Comment: 20+4 pages, 1 figure; v2: references added, typos corrected; v3:
typos corrected, JHEP versio
Dual S-matrix bootstrap. Part I. 2D theory
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We then explain how to optimize such bounds numerically, and prove that they provide the same bounds obtained from the usual primal formulation of the S-matrix Bootstrap, at least once convergence is attained from both perspectives. These techniques are then applied to the study of a gapped system with two stable particles of different masses, which serves as a toy model for bootstrapping popular physical systems
Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion
We study possible smooth deformations of the generalized free conformal field theory in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first nontrivial order in the
ε expansion, the anomalous dimensions of an infinite class of scalar local operators, without using the equations of motion. In the cases where other computational methods apply, the results agree
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