Celestial current algebra from Low’s subleading soft theorem
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Engineering topics
Strominger, Andrew
Publications and source records attributed to Strominger, Andrew.
Measuring color memory in a color glass condensate at electron–ion colliders
The color memory effect is the non-abelian gauge theory analog of the gravitational memory effect, in which the passage of color radiation induces a net relative SU(3) color rotation of a pair of nearby quarks. It is proposed that this effect can be measured in the Regge limit of deeply inelastic scattering at electron–ion colliders.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Conformally soft photons and gravitons
The four-dimensional S-matrix is reconsidered as a correlator on the celestial sphere at null infinity. Asymptotic particle states can be characterized by the point at which they enter or exit the celestial sphere as well as their SL(2, C) Lorentz quantum numbers: namely their conformal scaling dimension and spin h±h¯ instead of the energy and momentum. This characterization precludes the notion of a soft particle whose energy is taken to zero. We propose it should be replaced by the notion of a conformally soft particle with h = 0 or h¯ = 0. For photons we explicitly construct conformally soft SL(2, C) try on the celestial sphere. For gravity the generator of celestial conformal symmetry is constructed from a (2, 0) SL(2, C) primary wavefunction. Interestingly, BMS supertranslations are generated by a spin-one weight (3/2, 1/2) operator, which nevertheless shares holomorphic characteristics of a conformally soft operator. This is because the right hand side of its OPE with a weight (h, h¯) operator Oh,h¯ involves the shifted operator Oh+1/2,h¯+1/2. This OPE relation looks quite unusual from the celestial CFT 2 perspective but is equivalent to the leading soft graviton theorem and may usefully constrain celestial correlators in quantum gravity.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Black hole entropy and soft hair
A set of infinitesimal Virasoro L Ⓧ Virasoro R diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of ‘Wald-Zoupas’ counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges c L = c R = 12 J . Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.
79 ASTRONOMY AND ASTROPHYSICS↗
Soft factorization in QED from 2D Kac-Moody symmetry
The soft factorization theorem for 4D abelian gauge theory states that the S -matrix factorizes into soft and hard parts, with the universal soft part containing all soft and collinear poles. Similarly, correlation functions on the sphere in a 2D CFT with a U(1) Kac-Moody current algebra factorize into current algebra and non-current algebra factors, with the current algebra factor fully determined by its pole structure. In this paper, we show that these 4D and 2D factorizations are mathematically the same phenomena. The soft ‘t Hooft-Wilson lines and soft photons are realized as a complexified 2D current algebra on the celestial sphere at null infinity. The current algebra level is determined by the cusp anomalous dimension. The associated complex U(1) boson lives on a torus whose modular parameter is τ=$\frac{2πi}{e^2}$ + $\frac{θ}{2π}$. The correlators of this 2D current algebra fully reproduce the known soft part of the 4D S -matrix, as well as a conjectured generalization involving magnetic charges.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Color Memory: A Yang-Mills Analog of Gravitational Wave Memory
A transient color flux across null infinity in classical Yang-Mills theory is considered here. It is shown that a pair of test `quarks' initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For weak color flux the formula linearizes to the Fourier transform of the soft gluon theorem. Furthermore, this color memory effect is the Yang-Mills analog of the gravitational memory effect.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Gluon amplitudes as 2 d conformal correlators
Recently, spin-one wave functions in four dimensions that are conformal primaries of the Lorentz group S L ( 2 , C ) were constructed. Herein, we compute low-point, tree-level gluon scattering amplitudes in the space of these conformal primary wave functions. The answers show the same conformal covariance as correlators of spin-one primaries in a 2 d CFT. The Britto–Cachazo–Feng–Witten (BCFW) recursion relation between three- and four-point gluon amplitudes is recast into this conformal basis.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Infrared divergences in QED revisited
Recently it has been demonstrated that the vacuum state in QED is infinitely degenerate. Moreover a transition among the degenerate vacua is induced in any nontrivial scattering process and determined from the associated soft factor. Conventional computations of scattering amplitudes in QED do not account for this vacuum degeneracy and therefore always give zero. This vanishing of all conventional QED amplitudes is usually attributed to infrared divergences. In this work, we show that if these vacuum transitions are properly accounted for, the resulting amplitudes are nonzero and infrared finite. Our construction of finite amplitudes is mathematically equivalent to, and amounts to a physical reinterpretation of, the 1970 construction of Faddeev and Kulish.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
2D Stress Tensor for 4D Gravity
Here, we use the subleading soft-graviton theorem to construct an operator T z z whose insertion in the four-dimensional tree-level quantum gravity S matrix obeys the Virasoro-Ward identities of the energy momentum tensor of a two-dimensional conformal field theory ( CFT 2 ). Furthermore, the celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the CFT 2 , with the Lorentz group acting as the unbroken S L ( 2 , C ) subgroup.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Superrotation charge and supertranslation hair on black holes
It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass M, momentum $\vec{P}$, angular momentum $\vec{J}$ and boost charge $\vec{/k}$ , an infinite head of supertranslation hair. Furthermore, the distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with supertranslation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. We derive a leading-order Bondi-gauge expression for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Logarithmic corrections to black hole entropy from Kerr/CFT
It has been shown by A. Sen that logarithmic corrections to the black hole area-entropy law are entirely determined macroscopically from the massless particle spectrum. They therefore serve as powerful consistency checks on any proposed enumeration of quantum black hole microstates. Furthermore, Sen’s results include a macroscopic computation of the logarithmic corrections for a five-dimensional near extremal Kerr-Newman black hole. We compute these corrections microscopically using a stringy embedding of the Kerr/CFT correspondence and find perfect agreement.
79 ASTRONOMY AND ASTROPHYSICS↗
Higher-dimensional supertranslations and Weinberg’s soft graviton theorem
Asymptotic symmetries of theories with gravity in d = 2m + 2 spacetime dimensions are reconsidered for m > 1 in light of recent results concerning d = 4 BMS symmetries. Weinberg’s soft graviton theorem in 2m+2 dimensions is re-expressed as a Ward identity for the gravitational S-matrix. The corresponding asymptotic symmetries are identified with 2m + 2-dimensional supertranslations. An alternate derivation of these asymptotic symmetries as diffeomorphisms which preserve finite-energy boundary conditions at null infinity and act non-trivially on physical data is given. Our results differ from those of previous analyses whose stronger boundary conditions precluded supertranslations for d > 4. In conclusion, we find for all even d that supertranslation symmetry is spontaneously broken in the conventional vacuum and identify soft gravitons as the corresponding Goldstone bosons.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Asymptotic symmetries of massless QED in even dimensions
In this work, we consider the scattering of massless particles coupled to an abelian gauge field in 2n-dimensional Minkowski spacetime. Weinberg’s soft photon theorem is recast asWard identities for infinitely many new nontrivial symmetries of the massless QED S-matrix, with one such identity arising for each propagation direction of the soft photon. These symmetries are identified as large gauge transformations with angle-dependent gauge parameters that are constant along the null generators of null infinity. Almost all of the symmetries are spontaneously broken in the standard vacuum and the soft photons are the corresponding Goldstone bosons. In conclusion, our result establishes a relationship between soft theorems and asymptotic symmetry groups in any even dimension.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
2D Kac-Moody symmetry of 4D Yang-Mills theory
Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null in nity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. Furthermore, the Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null in nity and comprise the four-dimensional asymptotic symmetry group.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗