We analyze socalled generalized Veneziano and generalized Virasoro amplitudes. Under some physical assumptions, we find that their spectra must satisfy an overdetermined set of nonlinear recursion relations. The recursion relation for the generalized Veneziano amplitudes can be solved analytically and yields a twoparameter family which includes the Veneziano amplitude, the oneparameter family of Coon amplitudes, and a larger twoparameter family of amplitudes with an infinite tower of spins at each mass level. In the generalized Virasoro case, the only consistent solution is the string spectrum.
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A<sc>bstract</sc> 
A<sc>bstract</sc> We detail the properties of the Veneziano, Virasoro, and Coon amplitudes. These treelevel fourpoint scattering amplitudes may be written as infinite products with an infinite sequence of simple poles. Our approach for the Coon amplitude uses the mathematical theory of
q analysis. We interpret the Coon amplitude as aq deformation of the Veneziano amplitude for allq ≥ 0 and discover a new transcendental structure in its lowenergy expansion. We show that there is no analogousq deformation of the Virasoro amplitude. 
In this note we present a solution of N=4,d=7 gauged supergravity which is holographically dual to a codimension two defect living in a six dimensional SCFT. The solution is obtained by double analytic continuation of a two charge supersymmetric black hole solution. The condition that no conical deficits are present in the bulk and on the boundary is satisfied by a one parameter family of solutions for which some holographic observables are computed.more » « less

A bstract We revisit the proposal that the ensemble average over free boson CFTs in two dimensions — parameterized by Narain’s moduli space — is dual to an exotic theory of gravity in three dimensions dubbed U(1) gravity. We consider flavored partition functions, where the usual genus g partition function is weighted by Wilson lines coupled to the conserved U(1) currents of these theories. These flavored partition functions obey a heat equation which relates deformations of the Riemann surface moduli to those of the chemical potentials which measure these U(1) charges. This allows us to derive a SiegelWeil formula which computes the average of these flavored partition functions. The result takes the form of a “sum over geometries”, albeit with modifications relative to the unflavored case.more » « less

A bstract In this paper, we construct Janustype solutions of threedimensional gauged supergravity with sixteen supersymmetries. We find solutions which correspond to interfaces between the same CFT on both sides, as well as RGflow interfaces between CFTs with different numbers of supersymmetries and central charges. The solutions are obtained by solving the flow equations derived from the supersymmetry variations, and they preserve some fraction of the supersymmetries of the AdS 3 vacua.more » « less

A bstract Modular graph functions (MGFs) are SL(2 , ℤ)invariant functions on the Poincaré upper halfplane associated with Feynman graphs of a conformal scalar field on a torus. The lowenergy expansion of genusone superstring amplitudes involves suitably regularized integrals of MGFs over the fundamental domain for SL(2 , ℤ). In earlier work, these integrals were evaluated for all MGFs up to two loops and for higher loops up to weight six. These results led to the conjectured uniform transcendentality of the genusone fourgraviton amplitude in Type II superstring theory. In this paper, we explicitly evaluate the integrals of several infinite families of threeloop MGFs and investigate their transcendental structure. Up to weight seven, the structure of the integral of each individual MGF is consistent with the uniform transcendentality of string amplitudes. Starting at weight eight, the transcendental weights obtained for the integrals of individual MGFs are no longer consistent with the uniform transcendentality of string amplitudes. However, in all the cases we examine, the violations of uniform transcendentality take on a special form given by the integrals of triple products of nonholomorphic Eisenstein series. If Type II superstring amplitudes do exhibit uniform transcendentality, then the special combinations of MGFs which enter the amplitudes must be such that these integrals of triple products of Eisenstein series precisely cancel one another. Whether this indeed is the case poses a novel challenge to the conjectured uniform transcendentality of genusone string amplitudes.more » « less

Pure threedimensional gravity is a renormalizable theory with twofree parameters labelled by
andG $G$ .As a consequence, correlation functions of the boundary stress tensor inAdS\Lambda $\Lambda $ are uniquely fixed in terms of one dimensionless parameter, which is thecentral charge of the Virasoro algebra. The same argument implies thatAdS_3 ${}_{3}$ gravity at a finite radial cutoff is a renormalizable theory, but nowwith one additional parameter corresponding to the cutoff location. Thistheory is conjecturally dual to a_3 ${}_{3}$ deformedCFT, assuming that such theories actually exist. To elucidate this, westudy the quantum theory of boundary gravitons living on a cutoff planarboundary and the associated correlation functions of the boundary stresstensor. We compute stress tensor correlation functions to twoloop order(T\overline{T} $T\overline{T}$ being the loop counting parameter), extending existing tree levelresults. This is made feasible by the fact that the boundary gravitonaction simplifies greatly upon making a judicious field redefinition,turning into the NambuGoto action. After imposing Lorentz invariance,the correlators at this order are found to be unambiguous up to a singleundetermined renormalization parameter.G $G$ 
The purpose of this White Paper is to review recent progress towards elucidating and evaluating string amplitudes, relating them to quantum field theory amplitudes, applying their predictions to string dualities, exploring their connection with gravitational physics, and deepening our under standing of their mathematical structure. We also present a selection of targets for future research.more » « less

A bstract The contribution from even spin structures to the genustwo amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genustwo amplitude with four external NS states. The results agree with the parityeven NS components of a construction using chiral splitting and pure spinors given in earlier companion papers [29] and [33].more » « less

A bstract Motivated by applications to soft supersymmetry breaking, we revisit the expansion of the SeibergWitten solution around the multimonopole point on the Coulomb branch of pure SU( N ) $$ \mathcal{N} $$ N = 2 gauge theory in four dimensions. At this point N − 1 mutually local magnetic monopoles become massless simultaneously, and in a suitable duality frame the gauge couplings logarithmically run to zero. We explicitly calculate the leading threshold corrections to this logarithmic running from the SeibergWitten solution by adapting a method previously introduced by D’Hoker and Phong. We compare our computation to existing results in the literature; this includes results specific to SU(2) and SU(3) gauge theories, the large N results of Douglas and Shenker, as well as results obtained by appealing to integrable systems or topological strings. We find broad agreement, while also clarifying some lingering inconsistencies. Finally, we explicitly extend the results of Douglas and Shenker to finite N , finding exact agreement with our first calculation.more » « less