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Register a new userScale invariant Volkov-Akulov Supergravity
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A scale invariant Goldstino theory coupled to Supergravity is obtained as a standard supergravity dual of a rigidly scale invariant higher--curvature Supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.
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We construct a supergravity model whose scalar degrees of freedom arise from a chiral superfield and are solely a scalaron and an axion that is very heavy during the inflationary phase. The model includes a second chiral superfield $X$, which is subject however to the constraint $X^2=0$ so that it describes only a Volkov - Akulov goldstino and an auxiliary field. We also construct the dual higher - derivative model, which rests on a chiral scalar curvature superfield ${cal R}$ subject to the constraint ${cal R}^2=0$, where the goldstino dual arises from the gauge - invariant gravitino field strength as $gamma^{mn} {cal D}_m psi_n$. The final bosonic action is an $R+R^2$ theory involving an axial vector $A_m$ that only propagates a physical pseudoscalar mode.
We show that the two-dimensional $N=(2,2)$ Volkov-Akulov action that describes the spontaneous breaking of supersymmetry is a $Tbar{T}$ deformation of a free fermionic theory. Our findings point toward a possible relation between nonlinear supersymmetry and $T bar T$ flows.
We study scale invariance at the quantum level (three loops) in a perturbative approach. For a scale-invariant classical theory the scalar potential is computed at three-loop level while keeping manifest this symmetry. Spontaneous scale symmetry breaking is transmitted at quantum level to the visible sector (of $phi$) by the associated Goldstone mode (dilaton $sigma$) which enables a scale-invariant regularisation and whose vev $langlesigmarangle$ generates the subtraction scale ($mu$). While the hidden ($sigma$) and visible sector ($phi$) are classically decoupled in $d=4$ due to an enhanced Poincare symmetry, they interact through (a series of) evanescent couplings $proptoepsilon^k$, ($kgeq 1$), dictated by the scale invariance of the action in $d=4-2epsilon$. At the quantum level these couplings generate new corrections to the potential, such as scale-invariant non-polynomial effective operators $phi^{2n+4}/sigma^{2n}$ and also log-like terms ($propto ln^k sigma$) restoring the scale-invariance of known quantum corrections. The former are comparable in size to standard loop corrections and important for values of $phi$ close to $langlesigmarangle$. For $n=1,2$ the beta functions of their coefficient are computed at three-loops. In the infrared (IR) limit the dilaton fluctuations decouple, the effective operators are suppressed by large $langlesigmarangle$ and the effective potential becomes that of a renormalizable theory with explicit scale symmetry breaking by the usual DR scheme (of $mu=$constant).
We argue that accidental approximate scaling symmetries are robust predictions of weakly coupled string vacua, and show that their interplay with supersymmetry and other (generalised) internal symmetries underlies the ubiquitous appearance of no-scale supergravities in low-energy 4D EFTs. We identify 4 nested types of no-scale supergravities, and show how leading quantum corrections can break scale invariance while preserving some no-scale properties (including non-supersymmetric flat directions). We use these ideas to classify corrections to the low-energy 4D supergravity action in perturbative 10D string vacua, including both bulk and brane contributions. Our prediction for the Kahler potential at any fixed order in $alpha$ and string loops agrees with all extant calculations. p-form fields play two important roles: they spawn many (generalised) shift symmetries; and space-filling 4-forms teach 4D physics about higher-dimensional phenomena like flux quantisation. We argue that these robust symmetry arguments suffice to understand obstructions to finding classical de Sitter vacua, and suggest how to get around them in UV complete models.
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $phi$ in theories in which scale symmetry is broken only spontaneously by the dilaton ($sigma$). Its vev $langlesigmarangle$ generates the DR subtraction scale ($musimlanglesigmarangle$), which avoids the explicit scale symmetry breaking by traditional regularizations (where $mu$=fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($mu$=fixed scale). These operators have the form: $phi^6/sigma^2$, $phi^8/sigma^4$, etc, which generate an infinite series of higher dimensional polynomial operators upon expansion about $langlesigmaranglegg langlephirangle$, where such hierarchy is arranged by {it one} initial, classical tuning. These operators emerge at the quantum level from evanescent interactions ($proptoepsilon$) between $sigma$ and $phi$ that vanish in $d=4$ but are demanded by classical scale invariance in $d=4-2epsilon$. The Callan-Symanzik equation of the two-loop potential is respected and the two-loop beta functions of the couplings differ from those of the same theory regularized with $mu=$fixed scale. Therefore the running of the couplings enables one to distinguish between spontaneous and explicit scale symmetry breaking.
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