String theory in target space

205

288

We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden “totally positive” structure strikingly similar to the positive geometries associated with grassmannians and amplituhedra. This forces the infinite tower of higher-dimension operators to lie inside a new geometry we call the “EFT-hedron”. We initiate a systematic investigation of the boundary structure of the EFT-hedron, giving infinitely many linear and non-linear inequalities that must be satisfied by the EFT expansion in any theory. We illustrate the EFT-hedron geometry and constraints in a wide variety of examples, including new consistency conditions on the scattering amplitudes of photons and gravitons in the real world.

Section: Jhep05(2021)259mentioning

confidence: 99%

The EFT-hedron

Arkani-Hamed

Huang

2021

205

288

“…Note that it is known that monodromy relations, when combined with the asymptotic Regge behavior of string amplitudes, are sufficient to completely determine the four-particle amplitude [30]. In particular, the residue of the four-point amplitude is a single variable function, whose zeros on the real line can be completely determined by the monodromy relations.…”

Section: Jhep04(2021)195mentioning

confidence: 99%

“…is a common feature shared by all flat-space open string amplitudes for identical external states. In fact when combined with the asymptotic form of the Regge limit, the above relation is sufficient to completely fix the four-point amplitude [30]. In particular, using the monodromy relations, one can fix the residue of anyone of the factorization channel to a single variable function with the real zeros fixed.…”

Section: The Monodromy Planementioning

confidence: 99%

Carving out the space of open-string S-matrix

Huang

Liu

Rodina

et al. 2021

In this paper, we explore the open string amplitude’s dual role as a space-time S-matrix and a 2D holomorphic CFT correlation function. We pursue this correspondence in two directions. First, beginning with a general disk integrand dressed with a Koba-Nielsen factor, we demonstrate that exchange symmetry for the factorization residue of the amplitude forces the integrand to be expandable on SL(2,R) conformal blocks. Furthermore, positivity constraints associated with unitarity imply the SL(2,R) blocks must come in linear combinations for which the Virasoro block emerges at the “kink” in the space of solutions. In other words, Virasoro symmetry arises at the boundary of consistent factorization. Next, we consider the low energy EFT description, where unitarity manifests as the EFThedron in which the couplings must live. The existence of a worldsheet description implies, through the Koba-Nielsen factor, monodromy relations which impose algebraic identities amongst the EFT couplings. We demonstrate at finite derivative order that the intersection of the “monodromy plane” and the four-dimensional EFThedron carves out a tiny island for the couplings, which continues to shrink as the derivative order is increased. At the eighth derivative order, on a three-dimensional monodromy plane, the intersection fixes the width of this island to around 1.5% (of ζ(3)) and 0.2% (of ζ(5)) with respect to the toroidally compactified Type-I super string answer. This leads us to conjecture that the four-point open superstring amplitude can be completely determined by the geometry of the intersection of the monodromy plane and the EFThedron.

“…A more thorough treatment of on-shell amplitudes of arbitrary SO(d) irreps (in the context of the open bosonic string) can be found in [39].…”

Section: S-matrix Rule For Counting Structuresmentioning

confidence: 99%

Conformal correlators of mixed-symmetry tensors

Costa

Hansen

2015

Self Cite

113

150

We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to mixed-symmetry tensors by introducing a new commuting or anticommuting polarization vector for each row or column in the Young diagram that describes the index symmetries of the tensor. We determine the tensor structures that are allowed in n-point conformal correlation functions and give an algorithm for counting them in terms of tensor product coefficients. A simple derivation of the unitarity bound for arbitrary mixed-symmetry tensors is obtained by considering the conservation condition in embedding space. We show, with an example, how the new formalism can be used to compute conformal blocks of arbitrary external fields for the exchange of any conformal primary and its descendants. The matching between the number of tensor structures in conformal field theory correlators of operators in d dimensions and massive scattering amplitudes in d + 1 dimensions is also seen to carry over to mixed-symmetry tensors.