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Register a new userDouble-soft behavior of the dilaton of spontaneously broken conformal invariance
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The Ward identities involving the currents associated to the spontaneously broken scale and special conformal transformations are derived and used to determine, through linear order in the two soft-dilaton momenta, the double-soft behavior of scattering amplitudes involving two soft dilatons and any number of other particles. It turns out that the double-soft behavior is equivalent to performing two single-soft limits one after the other. We confirm the new double-soft theorem perturbatively at tree-level in a $D$-dimensional conformal field theory model, as well as nonperturbatively by using the gravity dual of ${cal{N}}=4$ super Yang-Mills on the Coulomb branch; i.e. the Dirac-Born-Infeld action on AdS${}_5 times S^5$.
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We consider the tree-level scattering amplitudes in the NS-NS (Neveu-Schwarz) massless sector of closed superstrings in the case where one external state becomes soft. We compute the amplitudes generically for any number of dimensions and any number and kind of the massless closed states through the subsubleading order in the soft expansion. We show that, when the soft state is a graviton or a dilaton, the full result can be expressed as a soft theorem factorizing the amplitude in a soft and a hard part. This behavior is similar to what has previously been observed in field theory and in the bosonic string. Differently from the bosonic string, the supersymmetric soft theorem for the graviton has no string corrections at subsubleading order. The dilaton soft theorem, on the other hand, is found to be universally free of string corrections in any string theory.
We explore the possibility that scale symmetry is a quantum symmetry that is broken only spontaneously and apply this idea to the Standard Model (SM). We compute the quantum corrections to the potential of the higgs field ($phi$) in the classically scale invariant version of the SM ($m_phi=0$ at tree level) extended by the dilaton ($sigma$). The tree-level potential of $phi$ and $sigma$, dictated by scale invariance, may contain non-polynomial effective operators, e.g. $phi^6/sigma^2$, $phi^8/sigma^4$, $phi^{10}/sigma^6$, etc. The one-loop scalar potential is scale invariant, since the loop calculations manifestly preserve the scale symmetry, with the DR subtraction scale $mu$ generated spontaneously by the dilaton vev $musimlanglesigmarangle$. The Callan-Symanzik equation of the potential is verified in the presence of the gauge, Yukawa and the non-polynomial operators. The couplings of the non-polynomial operators have non-zero beta functions that we can actually compute from the quantum potential. At the quantum level the higgs mass is protected by spontaneously broken scale symmetry, even though the theory is non-renormalizable. We compare the one-loop potential to its counterpart computed in the traditional DR scheme that breaks scale symmetry explicitly ($mu=$constant) in the presence at the tree level of the non-polynomial operators.
The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse) diffeomorphisms, linearized Weyl rescalings, and conformal transformations.
We perform a comprehensive study of on-shell recursion relations for Born amplitudes in spontaneously broken gauge theories and identify the minimal shifts required to construct amplitudes with a given particle content and spin quantum numbers. We show that two-line or three-line shifts are sufficient to construct all amplitudes with five or more particles, apart from amplitudes involving longitudinal vector bosons or scalars, which may require at most five-line shifts. As an application, we revisit selection rules for multi-boson amplitudes using on-shell recursion and little-group transformations.
We study the concomitant breaking of spatial translations and dilatations in Ginzburg-Landau-like models, where the dynamics responsible for the symmetry breaking is described by an effective Mexican hat potential for spatial gradients. We show that there are fractonic modes with either subdimensional propagation or no propagation altogether, namely, immobility. Such class of effective field theories encompasses instances of helical superfluids and meta-fluids, where fractons can be connected to an emergent symmetry under higher moment charges, leading in turns to the trivialization of some elastic coefficients. The introduction of a finite charge density alters the mobility properties of fractons and leads to a competition between the chemical potential and the superfluid velocity in determining the gap of the dilaton. The mobility of fractons can also be altered at zero density upon considering additional higher-derivative terms.
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