A bstract We compute 1 /λ corrections to the fourpoint functions of halfBPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 superYangMills theory at large N and large ’t Hooft coupling λ = $$ {g}_{\mathrm{YM}}^2N $$ g YM 2 N using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S 4 free energy, which was computed at leading order in large N and to all orders in 1 /λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1 /λ corrections to higher derivative corrections to supergravity for scattering amplitudes of KaluzaKlein scalars in IIB string theory on AdS 5 × S 5 , which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R 4 interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D 4 R 4 order. Combined with constraints from [1], our results can be used to derive CFT data to oneloop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in themore »
Twoloop superstring fivepoint amplitudes. Part II. Low energy expansion and Sduality
A bstract In an earlier paper, we constructed the genustwo amplitudes for five external massless states in Type II and Heterotic string theory, and showed that the α ′ expansion of the Type II amplitude reproduces the corresponding supergravity amplitude to leading order. In this paper, we analyze the effective interactions induced by Type IIB superstrings beyond supergravity, both for U(1) R preserving amplitudes such as for five gravitons, and for U(1) R violating amplitudes such as for one dilaton and four gravitons. At each order in α ′, the coefficients of the effective interactions are given by integrals over moduli space of genustwo modular graph functions, generalizing those already encountered for four external massless states. To leading and subleading orders, the coefficients of the effective interactions D 2 ℛ 5 and D 4 ℛ 5 are found to match those of D 4 ℛ 4 and D 6 ℛ 4 , respectively, as required by nonlinear supersymmetry. To the next order, a D 6 ℛ 5 effective interaction arises, which is independent of the supersymmetric completion of D 8 ℛ 4 , and already arose at genus one. A novel identity on genustwo modular graph functions, which we prove, more »
 Award ID(s):
 1914412
 Publication Date:
 NSFPAR ID:
 10228357
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2021
 Issue:
 2
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
More Like this


A bstract We study the fourpoint function of the lowestlying halfBPS operators in the $$ \mathcal{N} $$ N = 4 SU( N ) superYangMills theory and its relation to the flatspace fourgraviton amplitude in type IIB superstring theory. We work in a large N expansion in which the complexified YangMills coupling τ is fixed. In this expansion, nonperturbative instanton contributions are present, and the SL(2 , ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the massdeformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed $$ \mathcal{N} $$ N = 4 SYM theory, which in turn constrains the fourpoint correlator at separated points. In a normalization where the twopoint functions are proportional to N 2 − 1 and are independent of τ and $$ \overline{\tau} $$ τ ¯ , we find that the terms of order $$ \sqrt{N} $$ N and $$ 1/\sqrt{N} $$ 1 / N in the large N expansion of the fourpoint correlator are proportional to the nonholomorphic Eisenstein series $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ E 3 2 τ τ ¯ and $$more »

A bstract The full twoloop amplitudes for five massless states in Type II and Heterotic superstrings are constructed in terms of convergent integrals over the genustwo moduli space of compact Riemann surfaces and integrals of Green functions and Abelian differentials on the surface. The construction combines elements from the BRST cohomology of the pure spinor formulation and from chiral splitting with the help of loop momenta and homology invariance. The α ′ → 0 limit of the resulting superstring amplitude is shown to be in perfect agreement with the previously known amplitude computed in Type II supergravity. Investigations of the α ′ expansion of the Type II amplitude and comparisons with predictions from Sduality are relegated to a first companion paper. A construction from first principles in the RNS formulation of the genustwo amplitude with five external NS states is relegated to a second companion paper.

A bstract We study modular invariants arising in the fourpoint functions of the stress tensor multiplet operators of the $$ \mathcal{N} $$ N = 4 SU( N ) superYangMills theory, in the limit where N is taken to be large while the complexified YangMills coupling τ is held fixed. The specific fourpoint functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the $$ \mathcal{N} $$ N = 2 ∗ theory with respect to the squashing parameter b and mass parameter m , evaluated at the values b = 1 and m = 0 that correspond to the $$ \mathcal{N} $$ N = 4 theory on a round sphere. At each order in the 1 /N expansion, these fourth derivatives are modular invariant functions of ( τ, $$ \overline{\tau} $$ τ ¯ ). We present evidence that at halfinteger orders in 1 /N , these modular invariants are linear combinations of nonholomorphic Eisenstein series, while at integer orders in 1 /N , they are certain “generalized Eisenstein series” which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the lowenergy expansion of themore »

A bstract We study the singularity structure of twoloop QED amplitudes for the production of multiple offshell photons in massless electronpositron annihilation and develop counterterms that remove their infrared and ultraviolet divergences point by point in the loop integrand. The remainders of the subtraction are integrable in four dimensions and can be computed in the future with numerical integration. The counterterms capture the divergences of the amplitudes and factorize in terms of the Born amplitude and the finite remainder of the oneloop amplitude. They consist of simple one and twoloop integrals with at most three external momenta and can be integrated analytically in a simple manner with established methods. We uncover novel aspects of fully local IR factorization, where vertex and self energy subdiagrams must be modified by new symmetrizations over loop momenta, in order to expose their treelike tensor structures and hence factorization of IR singularities prior to loop integration. This work is a first step towards isolating locally the hard contributions of generic gauge theory amplitudes and rendering them integrable in exactly four dimensions with numerical methods.