Low energy expansion of the four-particle genus-one amplitude in type II superstring theory

Abstract This paper concerns a special class of n-point correlation functions of operators in the stress tensor supermultiplet of $$ \mathcal{N} $$ N = 4 supersymmetric SU(N) Yang-Mills theory. These are “maximal U(1)Y-violating” correlators that violate the bonus U(1)Y charge by a maximum of 2(n − 4) units. We will demonstrate that such correlators satisfy SL(2, ℤ)-covariant recursion relations that relate n-point correlators to (n − 1)-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-N expansion of n-point maximal U(1)Y-violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and (n − 4) chiral Lagrangian operators, starting from known properties of the n = 4 case. We concentrate on the first three orders in 1/N beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in AdS5× S5 at the same orders as R4, d4R4 and d6R4. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights (n − 4, 4 − n) that are SL(2, ℤ)-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to U(1)Y-violating n-particle interactions (n > 4) in the low-energy expansion of type IIB superstring amplitudes in AdS5× S5.

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CAN SST-II CONTAIN THE STANDARD MODEL?

Modern Physics Letters A ◽

10.1142/s0217732388001914 ◽

1988 ◽

Vol 03 (16) ◽

pp. 1603-1617

Author(s):

MITSUHIRO KATO ◽

TAKAO KOIKAWA ◽

MACHIKO TATEWAKI HATSUDA

Keyword(s):

Standard Model ◽

Dimensional Space ◽

Low Energy ◽

Type Ii ◽

Superstring Theory ◽

Energy Particle ◽

Moody Algebra ◽

The Standard Model ◽

Dimensional Space Time ◽

Particle Spectra

The answer to the title is ‘NO’. We investigate the low energy particle spectra of type-II superstring theory after compactification to 4 dimensional space-time by means of the super Kac-Moody algebra as well as the twisted super Kac-Moody algebra. We will show that there is no solution containing all of the particle contents in the standard model.

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

Journal of High Energy Physics ◽

10.1007/jhep02(2021)139 ◽

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.

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Nothing is certain in string compactifications

Journal of High Energy Physics ◽

10.1007/jhep12(2020)032 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Iñaki García Etxebarria ◽

Miguel Montero ◽

Kepa Sousa ◽

Irene Valenzuela

Keyword(s):

Flux Compactifications ◽

Spin Structure ◽

Energy Condition ◽

Low Energy ◽

Type Ii ◽

String Compactifications ◽

Compact Dimension ◽

Bordism Group ◽

Topological Obstruction ◽

M Theory

Abstract A bubble of nothing is a spacetime instability where a compact dimension collapses. After nucleation, it expands at the speed of light, leaving “nothing” behind. We argue that the topological and dynamical mechanisms which could protect a compactification against decay to nothing seem to be absent in string compactifications once supersymmetry is broken. The topological obstruction lies in a bordism group and, surprisingly, it can disappear even for a SUSY-compatible spin structure. As a proof of principle, we construct an explicit bubble of nothing for a T3 with completely periodic (SUSY-compatible) spin structure in an Einstein dilaton Gauss-Bonnet theory, which arises in the low-energy limit of certain heterotic and type II flux compactifications. Without the topological protection, supersymmetric compactifications are purely stabilized by a Coleman-deLuccia mechanism, which relies on a certain local energy condition. This is violated in our example by the nonsupersymmetric GB term. In the presence of fluxes this energy condition gets modified and its violation might be related to the Weak Gravity Conjecture.We expect that our techniques can be used to construct a plethora of new bubbles of nothing in any setup where the low-energy bordism group vanishes, including type II compactifications on CY3, AdS flux compactifications on 5-manifolds, and M-theory on 7-manifolds. This lends further evidence to the conjecture that any non-supersymmetric vacuum of quantum gravity is ultimately unstable.

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