A bstract We compute 1 /λ corrections to the four-point functions of half-BPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 super-Yang-Mills 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 Kaluza-Klein 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 one-loop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in themore »
Two-loop superstring five-point amplitudes. Part II. Low energy expansion and S-duality
A bstract In an earlier paper, we constructed the genus-two 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 genus-two modular graph functions, generalizing those already encountered for four external massless states. To leading and sub-leading 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 non-linear 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 genus-two modular graph functions, which we prove, more »
- Award ID(s):
- 1914412
- Publication Date:
- NSF-PAR ID:
- 10228357
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 2
- ISSN:
- 1029-8479
- Sponsoring Org:
- National Science Foundation
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A bstract We study the four-point function of the lowest-lying half-BPS operators in the $$ \mathcal{N} $$ N = 4 SU( N ) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large- N expansion in which the complexified Yang-Mills coupling τ is fixed. In this expansion, non-perturbative 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 mass-deformed 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 four-point correlator at separated points. In a normalization where the two-point 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 four-point correlator are proportional to the non-holomorphic Eisenstein series $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ E 3 2 τ τ ¯ and $$more »
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A bstract The full two-loop amplitudes for five massless states in Type II and Heterotic superstrings are constructed in terms of convergent integrals over the genus-two 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 S-duality are relegated to a first companion paper. A construction from first principles in the RNS formulation of the genus-two amplitude with five external NS states is relegated to a second companion paper.
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Publisher's Version of Record
- https://doi.org/10.1007/JHEP02(2021)139
