8,645 research outputs found
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
Four moments theorems on Markov chaos
We obtain quantitative Four Moments Theorems establishing convergence of the
laws of elements of a Markov chaos to a Pearson distribution, where the only
assumption we make on the Pearson distribution is that it admits four moments.
While in general one cannot use moments to establish convergence to a
heavy-tailed distributions, we provide a context in which only the first four
moments suffices. These results are obtained by proving a general carr\'e du
champ bound on the distance between laws of random variables in the domain of a
Markov diffusion generator and invariant measures of diffusions. For elements
of a Markov chaos, this bound can be reduced to just the first four moments.Comment: 24 page
Coclass theory for nilpotent semigroups via their associated algebras
Coclass theory has been a highly successful approach towards the
investigation and classification of finite nilpotent groups. Here we suggest a
similar approach for finite nilpotent semigroups. This differs from the group
theory setting in that we additionally use certain algebras associated to the
considered semigroups. We propose a series of conjectures on our suggested
approach. If these become theorems, then this would reduce the classification
of nilpotent semigroups of a fixed coclass to a finite calculation. Our
conjectures are supported by the classification of nilpotent semigroups of
coclass 0 and 1. Computational experiments suggest that the conjectures also
hold for the nilpotent semigroups of coclass 2 and 3.Comment: 13 pages, 2 figure
- …