Superstring theoryをめぐって(放談室)

A black hole may carry ``soft hair,'' low-energy quantum excitations that release information when the black hole evaporates.

/pdf/soft-hair-on-black-holes-1x4t0k0iud.pdf

Soft Hair on Black Holes

This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes. The lectures may be viewed online at this https URL. Please send typos or corrections to strominger@physics.this http URL.

Lectures on the Infrared Structure of Gravity and Gauge Theory

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U(1) gauge transformations that asymptotically approach an arbitrary function "(z, ¯ z) on the conformal sphere at future null infinity (I + ) but are independent of the retarded time. The value of " at past null infinity (I − ) is determined from that on I + by the condition that it take the same value at either end of any light ray crossing Minkowski space. The " 6 constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U(1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.

/pdf/new-symmetries-of-massless-qed-4gezzqsqhh.pdf

New Symmetries of Massless QED

The tree-level S-matrix of Einstein’s theory is known to have a representation as an integral over the moduli space of punctured spheres localized to the solutions of the scattering equations In this paper we introduce three operations that can be applied on the integrand in order to produce other theories Starting in d + M dimensions we use dimensional reduction to construct Einstein-Maxwell with gauge group U(1)
 M
  The second operation turns gravitons into gluons and we call it “squeezing” This gives rise to a formula for all multi-trace mixed amplitudes in Einstein-Yang-Mills Dimensionally reducing Yang-Mills we find the S-matrix of a special Yang-Mills-Scalar (YMS) theory, and by the squeezing operation we find that of a YMS theory with an additional cubic scalar vertex A corollary of the YMS formula gives one for a single massless scalar with a ϕ4 interaction Starting again from Einstein’s theory but in d + d dimensions we introduce a “generalized dimensional reduction” that produces the Born-Infeld theory or a special Galileon theory in d dimensions depending on how it is applied An extension of Born-Infeld formula leads to one for the Dirac-Born-Infeld (DBI) theory By applying the same operation to Yang-Mills we obtain the U(N ) non-linear sigma model (NLSM) Finally, we show how the Kawai-Lewellen-Tye relations naturally follow from our formulation and provide additional connections among these theories One such relation constructs DBI from YMS and NLSM

/pdf/scattering-equations-and-matrices-from-einstein-to-yang-2zdcpmie5i.pdf

Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM

Ambitwistor strings are chiral, infinite tension analogues of conventional string theory whose target space is the space of complex null geodesics and whose spectrum consists exclusively of massless states. At genus zero, these strings underpin the Cachazo- He-Yuan formulae for tree level scattering of gravitons, gluons and scalars. In this paper we extend these formulae in a number of directions. Firstly, we consider Ramond sector vertex operators and construct simple amplitudes involving space-time fermions. These agree with tree amplitudes in ten dimensional supergravity and super Yang-Mills. We then show that, after the usual GSO projections, the ambitwistor string partition function is modular invariant. We consider the scattering equations at genus one, and calculate one loop scattering amplitudes for NS-NS external states in the Type II ambitwistor string. We conjecture that these give new representations of (the integrand of) one loop supergravity amplitudes and we show that they have the expected behaviour under factorization of the worldsheet in both non-separating and separating degenerations.

/pdf/ambitwistor-strings-and-the-scattering-equations-at-one-loop-4sekcc03wq.pdf

Ambitwistor strings and the scattering equations at one loop

In this short note I show that the soft limit for colour-ordered tree-level Yang- Mills amplitudes contains a sub-leading divergent term. This term is analogous to those found recently by Cachazo and Strominger for tree-level gravity amplitudes.

/pdf/soft-sub-leading-divergences-in-yang-mills-amplitudes-41f8v8p6gp.pdf

Soft sub-leading divergences in Yang-Mills amplitudes

We describe new ambitwistor string theories that give rise to the recent am- plitude formulae for Einstein-Yang-Mills, (Dirac)-Born-Infeld, Galileons and others intro- duced by Cachazo, He and Yuan. In the case of the Einstein-Yang-Mills amplitudes, an important role is played by a novel worldsheet conformal eld theory that provides the ap- propriate colour factors precisely without the spurious multitrace terms of earlier models that had to be ignored by hand. This is needed to obtain the correct multitrace terms that arise when Yang-Mills is coupled to gravity.

/pdf/new-ambitwistor-string-theories-3gooh9964p.pdf

New ambitwistor string theories

In this paper we present the null string origin of the ambitwistor string. Classically, the null string is the tensionless limit of string theory, and so too is the ambitwistor string. Both have as constraint algebra the Galilean Conformal Algebra in two dimensions. But something interesting happens in the quantum theory since there is an ambiguity in quantizing the null string. We show that, given a particular choice of quantization scheme and a particular gauge, the null string coincides with the ambitwistor string both classically and quantum mechanically. We also show that the same holds for the spinning versions of the null string and ambitwistor string. With these results we clarify the relationship between the ambitwistor string, the null string, the usual string and the Hohm-Siegel-Zwiebach theory.

/pdf/on-the-null-origin-of-the-ambitwistor-string-6h0j8cbxpq.pdf

On the null origin of the ambitwistor string

Perturbatively around flat space, the scattering amplitudes of gravity are related to those of Yang–Mills by colour-kinematic duality, under which gravitational amplitudes are obtained as the ‘double copy’ of the corresponding gauge theory amplitudes. We consider the question of how to extend this relationship to curved scattering backgrounds, focusing on certain ‘sandwich’ plane waves. We calculate the 3-point amplitudes on these backgrounds and find that a notion of double copy remains in the presence of background curvature: graviton amplitudes on a gravitational plane wave are the double copy of gluon amplitudes on a gauge field plane wave. This is non-trivial in that it requires a non-local replacement rule for the background fields and the momenta and polarization vectors of the fields scattering on the backgrounds. It must also account for new ‘tail’ terms arising from scattering off the background. These encode a memory effect in the scattering amplitudes, which naturally double copies as well.

Eduardo Casali

Papers

Ambitwistor strings and the scattering equations at one loop

Soft sub-leading divergences in Yang-Mills amplitudes

New ambitwistor string theories

On the null origin of the ambitwistor string

Scattering on plane waves and the double copy