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In this study, we investigate various deformations within the framework of Bondi-van der Burg-Metzner-Sachs invariant field theory (BMSFT). Specifically, we explore the impact of Bondi-van der Burg-Metzner-Sachs (BMS) symmetry on the theory by introducing key deformations, namely, $T \overline{T}$, $JT_{\mu}$, and $\sqrt{T \overline{T}}$ deformations. In the context of generic seed theories possessing BMS symmetry, we derive the first-order correction of correlation functions using the systematic application of BMS symmetry ward identities. However, it is worth noting that higher-order corrections are intricately dependent on the specific characteristics of the seed theories. To illustrate our findings, we select the BMS free scalar and free fermion as representative seed theories. We then proceed to analytically determine the deformed action by solving the nontrivial flow equations. Additionally, we extend our analysis to include second-order deformations within these deformed theories., Comment: 54 pages, 0 figure

Four-dimensional all-loop amplitudes in QED and gravity exhibit universal Infrared (IR) singularities with a factorization structure. This structure is governed by tree amplitudes and a universal IR-divergent factor representing the exchange of soft particles between external lines. This letter offers a precise dual interpretation of these universal IR-divergent factors within celestial holography. Considering the tree amplitude as the foundation of the celestial conformal field theory (CCFT), these universal factors correspond to marginal deformations with a \textit{double-current} construction in the CCFT. Remarkably, a novel geometric representation of these deformations through topological gauging provides an exact description of transitions within bulk vacuum moduli spaces which extends the celestial holography beyond the perturbative level. Our findings establish a concrete dictionary for celestial holography and offer a holographic lens to understand loop corrections in scattering amplitudes., Comment: v3: 10 pages + appendices, discussions extended, refs. added, accepted for publication in PRD as a Letter

In this paper, we derive a $T\bar{T}$ deformed soft graviton theorem in the context of celestial holography. As a concrete example, it illustrates that a two-dimensional irrelevant deformation can be applied to a four-dimensional theory at the level of amplitudes. We argue that the $T\bar{T}$ deformation has a close relation to the loop-correction from the amplitude side which could provide an alternative way to construct an ultraviolet complete quantum theory of gravity., Comment: v2: Interpretation improved significantly, discussions on the connection between loop corrections and deformations added, extra with respect to the version accepted for publication in journal due to the page limits