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Abstract Weakly nonlinear, bi‐periodic patterns of waves that propagate in the‐direction with amplitude variation in the‐direction are generated in a laboratory. The amplitude variation in the‐direction is studied within the framework of the vector (vNLSE) and scalar (sNLSE) nonlinear Schrödinger equations using the uniform‐amplitude, Stokes‐like solution of the vNLSE and the Jacobi elliptic sine function solution of the sNLSE. The wavetrains are generated using the Stokes‐like solution of vNLSE; however, a comparison of both predictions shows that while they both do a reasonably good job of predicting the observed amplitude variation in, the comparison with the elliptic function solution of the sNLSE has significantly less error when the ratio of‐wavenumber to the two‐dimensional wavenumber is less than about 0.25. For ratios between about 0.25 and 0.30 (the limit of the experiments), the two models have comparable errors. When the ratio is less than about 0.17, agreement with the vNLSE solution requires a third‐harmonic term in the‐direction, obtained from a Stokes‐type expansion of interacting, symmetric wavetrains. There is no evidence of instability growth in the‐direction, consistent with the work of Segur and colleagues, who showed that dissipation stabilizes the modulational instability. Finally, there is some extra amplitude variation in, which is examined via a qualitative stability calculation that allows symmetry breaking in that direction.
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The Boundaries of KKLT
Abstract We consider the conundrum of generating de Sitter space from higher‐dimensional geometry, with particular attention to KKLT‐type constructions[3] and their 5d implications. We show that even in the probe approximation with small, a consistent higher‐dimensional solution requires a deformation of a modulus field playing the role of a Goldberger‐Wise stabilizing field in Randall‐Sundrum type geometries that occurs through a shift in a the throat length. We identify the light radion field that sets the length of the throat, whose origin is the dynamical conifold deformation parameter. By analyzing the theory as a 5d model of mismatched branes in AdS5 space with a GW stabilization mechanism, we show how energy (and supersymmetry breaking) is transferred to both the IR and UV regions of the throat to generate a consistent 4d de Sitter sliced geometry. This should help resolve some of the recent apparent paradoxes in explicit higher‐dimensional constructions. Moreover, the radion gives insight into the potential for the previously identified “conifold instability”. We argue that this instability would be a destabilization of the potential for the radion in KKLT, which can occur when the perturbation is too large. If indeedis too small, the radion would enter on its runaway direction and the conifold deformation would shrink to zero size. It is difficult to satisfy the required bound and a) maintain a hierarchy in the simpler CY manifolds and b) complete the cosmological phase transition into the stabilized throat, We also discuss the implications of this type of setup for supersymmetry breaking, and how multiple throats can introduce hierarchies of supersymmetry breaking masses, even in an anomaly‐mediated scenario. In an appendix we consider general compactification constraints.
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- Award ID(s):
- 1915071
- PAR ID:
- 10133668
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Fortschritte der Physik
- Volume:
- 68
- Issue:
- 3-4
- ISSN:
- 0015-8208
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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