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A<sc>bstract</sc> In this paper, we analyze the loop corrections to celestial OPE for gluons and gravitons. Even at the loop level, the soft gluons and gravitons have conformal dimensions ∆ = 1−$${\mathbb{Z}}_{\ge 0}$$. The only novelty is the presence of higher poles. At one loop level, there are two types of conformal soft gluons with a single pole and a double pole in the ∆ plane. The celestial OPEs are obtained using the collinear splitting functions. In the case of gluons, the splitting functions receive loop corrections. After taking the holomorphic soft limit, we find the OPE of conformal soft gluons. We find a novel mixing of simple and double poles soft gluon operators in the OPE. In the case of gravitons, where splitting functions are known to be all loop exact, we still find a wedge algebra ofw∞which is in addition to the wedge algebra ofw1+∞already found by Strominger.
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Poles and Branch Cuts in Free Surface Hydrodynamics
We consider the motion of ideal incompressible fluid with free surface. We analyzed the exact fluid dynamics through the time-dependent conformal mapping z=x+iy=z(w,t) of the lower complex half plane of the conformal variable w into the area occupied by fluid. We established the exact results on the existence vs. nonexistence of the pole and power law branch point solutions for 1/zw and the complex velocity. We also proved the nonexistence of the time-dependent rational solution of that problem for the second- and the first-order moving pole.
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- PAR ID:
- 10181346
- Date Published:
- Journal Name:
- Water Waves
- ISSN:
- 2523-367X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s42286-020-00040-y
