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Register a new userSUSY and Flat Direction in de Sitter Space
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M. Tanaka
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We have found that supersymmetry (SUSY) in curved space is broken softly. It is also found that Pauli-Villars regularization preserves the remaining symmetry, softly broken SUSY. Using it we computed the one-loop effective potential along a (classical) flat direction in a Wess-Zumino model in de Sitter space. The analysis is relevant to the Affleck-Dine mechanism for baryogenesis. The effective potential is unbounded from below: $V_{eff}(phi)to -3g^2H^2phi ^2 ln phi ^2 /16pi ^2$, where $phi$ is the scalar field along the flat direction, g is a typical coupling constant, and H is the Hubble parameter. This is identical with the effective potential which is obtained by using proper-time cutoff regularization. Since proper-time cutoff regularization is exact even at the large curvature region, the effective potential possesses softly broken SUSY and reliability in the large curvature region.
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Maximally symmetric curved-brane solutions are studied in dilatonic braneworld models which realise the self-tuning of the effective four-dimensional cosmological constant. It is found that no vacua in which the brane has de Sitter or anti-de Sitter geometry exist, unless one modifies the near-boundary asymptotics of the bulk fields. In the holographic dual picture, this corresponds to coupling the UV CFT to a curved metric (possibly with a defect). Alternatively, the same may be achieved in a flat-space QFT with suitable variable scalar sources. With these ingredients, it is found that maximally symmetric, positive and negative curvature solutions with a stabilised brane position generically exist. The space of such solutions is studied in two different types of realisations of the self-tuning framework. In some regimes we observe a large hierarchy between the curvature on the brane and the boundary UV CFT curvature. This is a dynamical effect due to the self-stabilisation mechanism. This setup provides an alternative route to realising de Sitter space in string theory.
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In this note, we study the holographic CFT in the de Sitter static patch at finite temperature $T$ and chemical potential. We find that butterfly velocity $v_B$ in such field theory degenerates for all values of the Hubble parameter $H$ and $T$. We interpret this as a chaos disruption caused by the interplay between the expansion of chaotic correlations constrained by $v_B$ and effects caused by de Sitter curvature. The chemical potential restores healthy butterfly velocity for some range of temperatures. Also, we provide some analogy of this chaos suppression with the Schwinger effect in de Sitter and black hole formation from shock wave collision.
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We study the consistency of the cubic couplings of a (partially-)massless spinning field to two scalars in $left(d+1right)$-dimensional de Sitter space. Gauge invariance of observables with external (partially)-massless spinning fields translates into Ward-Takahashi identities on the boundary. Using the Mellin-Barnes representation for boundary correlators in momentum space, we give a systematic study of Ward-Takahashi identities for tree-level 3- and 4-point processes involving a single external (partially-)massless field of arbitrary integer spin-$J$. 3-point Ward-Takahashi identities constrain the mass of the scalar fields to which a (partially-)massless spin-$J$ field can couple. 4-point Ward-Takahashi identities then constrain the corresponding cubic couplings. For massless spinning fields, we show that Weinbergs flat space results carry over to $left(d+1right)$-dimensional de Sitter space: For spins $J=1,2$ gauge-invariance implies charge-conservation and the equivalence principle while, assuming locality, higher-spins $J>2$ cannot couple consistently to scalar matter. This result also applies to anti-de Sitter space. For partially-massless fields, restricting for simplicity to those of depth-2, we show that there is no consistent coupling to scalar matter in local theories. Along the way we give a detailed account of how contact amplitudes with and without derivatives are represented in the Mellin-Barnes representation. Various new explicit expressions for 3- and 4-point functions involving (partially-)massless fields and conformally coupled scalars in dS$_4$ are given.
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