scholarly journals One-loop same helicity four-point amplitude from shifts

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Pratik Chattopadhyay ◽  
Kirill Krasnov
Keyword(s):  
Point Amplitude

scholarly journals On the N-pion extension of the Lovelace-Shapiro model

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Massimo Bianchi ◽  
Dario Consoli ◽  
Paolo Di Vecchia
Keyword(s):  
Extra Dimensions ◽  
Tree Level ◽  
Negative Norm ◽  
Projective Invariance ◽  
Non Linear ◽  
Point Amplitude

Abstract We reconsider a modification of the N-point amplitude of the Neveu-Schwarz (NS) model in which the tachyon becomes a pion by shifting its mass to zero and keeping the super-projective invariance of the integrand of the amplitude. For the scattering of four particles it reduces to the amplitude written by Lovelace and Shapiro that has Adler zeroes. We confirm that also the N-pion amplitude has Adler zeroes and show that it reduces to that of the non-linear σ-model for α′ → 0 keeping Fπ fixed. The four- and six-point flavour-ordered amplitudes satisfy tree-level unitarity since they can be derived from the correspondent amplitudes of the NS model in ten dimensions by suitably choosing the components of the momenta of the external mesons in the six extra dimensions. Negative norm states (ghosts) are shown to appear instead in higher-point amplitudes. We also discuss several amplitudes involving different external mesons.

scholarly journals Two-loop superstring five-point amplitudes. Part II. Low energy expansion and S-duality

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Eric D’Hoker ◽  
Carlos R. Mafra ◽  
Boris Pioline ◽  
Oliver Schlotterer
Keyword(s):  
Moduli Space ◽  
Effective Interaction ◽  
Type Ii ◽  
Leading Order ◽  
Effective Interactions ◽  
Heterotic String Theory ◽  
Genus Two ◽  
Genus One ◽  
Graph Function ◽  
Point Amplitude

Abstract 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 D2ℛ5 and D4ℛ5 are found to match those of D4ℛ4 and D6ℛ4, respectively, as required by non-linear supersymmetry. To the next order, a D6ℛ5 effective interaction arises, which is independent of the supersymmetric completion of D8ℛ4, and already arose at genus one. A novel identity on genus-two modular graph functions, which we prove, ensures that up to order D6ℛ5, the five-point amplitudes require only a single new modular graph function in addition to those needed for the four-point amplitude. We check that the supergravity limit of U(1)R-violating amplitudes is free of UV divergences to this order, consistently with the known structure of divergences in Type IIB supergravity. Our results give strong consistency tests on the full five-point amplitude, and pave the way for understanding S-duality beyond the BPS-protected sector.

scholarly journals All-loop-orders relation between Regge limits of $$ \mathcal{N} $$ = 4 SYM and $$ \mathcal{N} $$ = 8 supergravity four-point amplitudes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Stephen G. Naculich
Keyword(s):  
Infrared Divergence ◽  
Loop Order ◽  
Loop Correction ◽  
Divergence Structure ◽  
Regge Limit ◽  
Point Amplitude

Abstract We examine in detail the structure of the Regge limit of the (nonplanar) $$ \mathcal{N} $$ N = 4 SYM four-point amplitude. We begin by developing a basis of color factors Cik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through $$ \mathcal{O}\left({\upepsilon}^2\right) $$ O ϵ 2 at two loops, and through $$ \mathcal{O}\left({\upepsilon}^0\right) $$ O ϵ 0 at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the $$ \mathcal{N} $$ N = 8 supergravity four-point amplitude.

scholarly journals Complete four-loop four-point amplitude inN=4super-Yang-Mills theory

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
Z. Bern ◽  
J. J. M. Carrasco ◽  
L. J. Dixon ◽  
H. Johansson ◽  
R. Roiban
Keyword(s):  
Yang Mills ◽  
Point Amplitude

scholarly journals The three-loop MHV octagon from $$ \overline{Q} $$ equations

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Zhenjie Li ◽  
Chi Zhang
Keyword(s):  
Yang Mills ◽  
Remainder Function ◽  
Point Amplitude

Abstract The $$ \overline{Q} $$ Q ¯ equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory. By using the $$ \overline{Q} $$ Q ¯ equations, we compute the symbol of the first MHV amplitude with algebraic letters — the three-loop 8-point amplitude (or the octagon remainder function) — in this theory. The symbol alphabet for this amplitude consists of 204 independent rational letters and shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.

EVOLUTION OF CONFORMAL COLOR DIPOLES AND HIGH-ENERGY AMPLITUDES IN $\mathcal{N} = 4$ SYM

2011 ◽  
Vol 04 ◽  
pp. 9-19
Author(s):  
IAN BALITSKY
Keyword(s):  
Perturbation Theory ◽  
Wilson Line ◽  
Energy Operator ◽  
High Energy ◽  
Conformal Structure ◽  
Coefficient Function ◽  
Large N ◽  
Energy Behavior ◽  
Regge Limit ◽  
Point Amplitude

The high-energy behavior of the [Formula: see text] SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large Nc, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the first two orders in coupling constant: BFKL intercept and NLO BFKL intercept calculated in Ref. [1]. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four Z2 currents in the first two orders in perturbation theory.

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