We utilize dispersion relations to constrain weakly coupled ultraviolet (UV) completions of gravity when the external particles are scalars with color or flavor indices. We furnish a sum rule which implies that only certain patterns of representations can be ommitted in the UV. For adjoint scalars coupled to gravity, this predicts new particles, or the breaking of the symmetry, in the UV. This is all derived from the boundedness required for the dispersion relation, covariance with the underlying symmetries, and crossing symmetry. Unitarity is not invoked to derive the vanishing constraint.
Extending previous work on a dual resonant bootstrap which has the Veneziano amplitude as its unique solution, we motivate a closed string analogue of the bootstrap which inspires novel deformations of the Virasoro-Shapiro amplitude. This amplitude interpolates between the corners of the EFT-hedron defined by Caron-Huot and Van Duong and sweeps out EFT coefficient trajectories beyond the trivial higher-spin region.
We motivate an analytic bootstrap which defines algebraic varities whose solutions are multi-parameter families of dual resonant tree-level amplitudes. Imposing the strongest form of our assumptions leaves only a single point, the Veneziano amplitude. This defines simple conditions under which the Veneziano amplitude is the unique consistent solution to a bootstrap problem.
This letter considers an ab initio construction of the differential equation rules described in its longer companion paper on differential equations and cosmological correlators. Through time evolutions encoding in the structure of kinematic differential equations we present an abstract context, divorced from explicit time-integral representations of correlators, in which consistent time evolution emerges from a set of combinatorial rules.
We study the differential equations obeyed by conformally coupled scalars in power-law FRW cosmologies in the context of twisted cohomology, which reduces the problem to identifying the entries of a certain matrix as a function of kinematic data. We present a set of graphical rules which faciliate the algorithmic and efficient computation of the entries of this matrix. This framing presents furnishes a graphical context in which to understand the time evolution encoded in the kinematic differential equations obeyed by cosmological correlators.
We present a subtraction scheme for ultraviolet (UV) divergent, infrared (IR) safe scalar Feynman integrals in dimensional regularization with any number of scales. This is done by introducing u-variables, inspired by structures found studying the open-string moduli space, and results in an algorithmic prescription for the computation of a set of convergent integrals, dressed by powers of epsilon, which calculate the Feynman integral in dimensional regularization. This is the first general solution to this problem.
We study a class of tree-level Ansätze for two-to-two scalar and gauge boson amplitudes inspired by stringy UV completions. These amplitudes are Regge bounded and exponentially soft, but not manifestly unitary. Unitarity constitues a non-trivial consistency condition on the couplings, which we impose to derive suprising constraints. In particular, in dimensions between five and ten we find that the maximm allowed rank of the gauge group agrees exactly with a conjecture from the swampland program. This fact is non-trivially true for both SO(N) and SU(N) gauge groups.
We define a class of Newton polytopes which characterize UV and IR divergences of Feynman integrals. This framework also exposes new patterns of IR singularities. In the context of tropical geometry, this furnishes a prescription to compute the leading divergence of such Feynman integrals in dimensional regularization.
In this note we report an improved determination of the scaling dimensions and OPE coefficients of the minimal supersymmetric extension of the 3d Ising model using the conformal bootstrap. We also show how this data can be used as input to the Lorentzian inversion formula, finding good agreement between analytic calculations and numerical extremal spectra once mixing effects are resolved.
We present a new "differential" representation of the cosmological wavefunction in de Sitter spacetime that obviates this problem for a large class of phenomenologically relevant theories. Given any tree-level Feynman-Witten diagram, we give simple algebraic rules to write down a seed function and a differential operator that transforms it into the desired wavefunction coefficient for any scale-invariant, parity-invariant theory of massless scalars and gravitons with general boost-breaking interactions. In particular, this applies to large classes of phenomenologically relevant theories such as those described by the effective field theory of inflation or solid inflation.
We present a recursive rule for the symbol of perturbative contributions to the vacuum wave function of a conformally coupled scalar in FRW cosmologies. The rule applies exactly for conformally coupled scalars with a cubic interaction in four-dimensional de Sitter space, a case of particular relevance as a source of building blocks for inflationary correlators. We use the rule to efficiently reproduce the tree-level four-point contribution and present novel computations of the bubble integrand and the tree-level five-point contribution. Our results apply equally well to the computation of Witten diagrams in Euclidean AdS.
We utilize the conformal bootstrap to study constraints on three-dimensional conformalm field theories with a Z2 or parity symmetry, assuming a single relevant scalar invariant under the symmetry. When there is an additional relevant odd scalar, we map out the space of such "Ising-like" CFTs. Allowing a second relevant odd scalar, we identify a feature in the space, and conjecture it to be the location of the minimal supersymmetric extension of the Ising model.