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 Poisson equation for genus two string invariants: a conjecture

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Anirban Basu
Keyword(s):  
String Theory ◽  
Poisson Equation ◽  
Moduli Space ◽  
Asymptotic Expansions ◽  
Riemann Surfaces ◽  
Type Ii ◽  
Genus Two

Abstract We consider some string invariants at genus two that appear in the analysis of the D8ℛ4 and D6ℛ5 interactions in type II string theory. We conjecture a Poisson equation involving them and the Kawazumi-Zhang invariant based on their asymptotic expansions around the non-separating node in the moduli space of genus two Riemann surfaces.

scholarly journals Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds

2019 ◽  
Vol 7 (3) ◽  
Author(s):  
Guillaume Bossard ◽  
Charles Cosnier-Horeau ◽  
Boris Pioline
Keyword(s):  
Black Holes ◽  
Effective Interaction ◽  
Three Dimensional ◽  
Theta Series ◽  
Siegel Modular Form ◽  
Tree Level ◽  
Type I ◽  
Type Ii ◽  
Effective Interactions ◽  
Perturbative Corrections

Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the \nabla^2(\nabla\phi)^4∇2(∇ϕ)4 effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact degeneracies of 1/4-BPS dyons. We show that this Ansatz reproduces the known perturbative corrections at weak heterotic coupling, including tree-level, one- and two-loop corrections, plus non-perturbative effects of order e^{-1/g_3^2}e−1/g32. We also examine the weak coupling expansions in type I and type II string duals and find agreement with known perturbative results, . In the limit where a circle in the internal torus decompactifies, our Ansatz predicts the exact \nabla^2 F^4∇2F4 effective interaction in four-dimensional CHL string vacua, along with infinite series of exponentially suppressed corrections of order e^{-R}e−R from Euclideanized BPS black holes winding around the circle, and further suppressed corrections of order e^{-R^2}e−R2 from Taub-NUT instantons. We show that instanton corrections from 1/4-BPS black holes are precisely weighted by the BPS index predicted from the DVV formula, including the detailed moduli dependence. We also extract two-instanton corrections from pairs of 1/2-BPS black holes, demonstrating consistency with supersymmetry and wall-crossing, and estimate the size of instanton-anti-instanton contributions.

scholarly journals FORMAL RELATION AMONG VARIOUS HERMITIAN AND NON-HERMITIAN EFFECTIVE INTERACTIONS

2005 ◽  
Vol 14 (01) ◽  
pp. 21-28 ◽  
Author(s):  
RYOJI OKAMOTO ◽  
SHINICHIRO FUJII ◽  
KENJI SUZUKI
Keyword(s):  
Effective Interaction ◽  
Model Space ◽  
General Definition ◽  
Effective Interactions ◽  
Formal Relation ◽  
Definition Of ◽  
Effective Hamiltonians

A general definition of the model-space effective interaction is given. The energy-independent effective Hamiltonians derived in a time-independent way are classified systematically.

scholarly journals Moduli spaces of non-geometric type II/heterotic dual pairs

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Yoan Gautier ◽  
Dan Israël
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Type Ii ◽  
Duality Group ◽  
Dual Pairs ◽  
Perturbative Correction ◽  
Singularity Structure ◽  
Four Dimensions ◽  
Geometric Type ◽  
Perturbative Corrections

Abstract We study the moduli spaces of heterotic/type II dual pairs in four dimensions with $$ \mathcal{N} $$ N = 2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non- perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in α′.

Volume transition effects on the correlations and effective interactions among highly charged microgels

Soft Matter ◽  
2020 ◽  
Vol 16 (21) ◽  
pp. 5081-5093 ◽  
Author(s):  
L. A. Aguirre-Manzo ◽  
P. González-Mozuelos
Keyword(s):  
Effective Interaction ◽  
Counterion Condensation ◽  
Effective Interactions ◽  
Volume Transition ◽  
Transition Effects

Microgels shrinkage promotes counterion condensation, which in the highly charged regime markedly inhibits the effective interaction and induces strong counterion–counterion correlations that deviate this potential from the traditional Yukawa shape.

scholarly journals On TCS G2 manifolds and 4D emergent strings

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Fengjun Xu
Keyword(s):  
Moduli Space ◽  
Quantum Corrections ◽  
Type Ii ◽  
Quantum Level ◽  
Weakly Coupled ◽  
G2 Manifolds ◽  
Fundamental Type ◽  
M Theory ◽  
Distance Limit ◽  
Refined Version

Abstract In this note, we study the Swampland Distance Conjecture in TCS G2 manifold compactifications of M-theory. In particular, we are interested in testing a refined version — the Emergent String Conjecture, in settings with 4d N = 1 supersymmetry. We find that a weakly coupled, tensionless fundamental heterotic string does emerge at the infinite distance limit characterized by shrinking the K3-fiber in a TCS G2 manifold. Such a fundamental tensionless string leads to the parametrically leading infinite tower of asymptotically massless states, which is in line with the Emergent String Conjecture. The tensionless string, however, receives quantum corrections. We check that these quantum corrections do modify the volume of the shrinking K3-fiber via string duality and hence make the string regain a non-vanishing tension at the quantum level, leading to a decompactification. Geometrically, the quantum corrections modify the metric of the classical moduli space and are expected to obstruct the infinite distance limit. We also comment on another possible type of infinite distance limit in TCS G2 compactifications, which might lead to a weakly coupled fundamental type II string theory.

FIVEBRANE STRUCTURES

2009 ◽  
Vol 21 (10) ◽  
pp. 1197-1240 ◽  
Author(s):  
HISHAM SATI ◽  
URS SCHREIBER ◽  
JIM STASHEFF
Keyword(s):  
String Theory ◽  
Heterotic String ◽  
Target Space ◽  
Type Ii ◽  
Anomaly Cancellation ◽  
Heterotic String Theory ◽  
Dual Version ◽  
String Structure ◽  
Topological Obstructions ◽  
The One

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green–Schwarz anomaly cancellation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancellation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancellation points to a relation of string and Fivebrane structures under electric-magnetic duality.

Type II compact almost homogeneous manifolds of cohomogeneity one-II

2019 ◽  
Vol 30 (13) ◽  
pp. 1940002
Author(s):  
Daniel Guan
Keyword(s):  
Moduli Space ◽  
Kähler Manifold ◽  
Type Ii ◽  
Homogeneous Manifolds ◽  
Kähler Metrics ◽  
Cohomogeneity One ◽  
Kahler Metrics ◽  
Kahler Manifold ◽  
Blowing Up ◽  
Compact Kähler Manifold

In this paper, we start the program of the existence of the smooth equivariant geodesics in the equivariant Mabuchi moduli space of Kähler metrics on type II cohomogeneity one compact Kähler manifold. In this paper, we deal with the manifolds [Formula: see text] obtained by blowing up the diagonal of the product of two copies of a [Formula: see text].

scholarly journals Computing theta functions in quasi-linear time in genus two and above

2016 ◽  
Vol 19 (A) ◽  
pp. 163-177
Author(s):  
Hugo Labrande ◽  
Emmanuel Thomé
Keyword(s):  
Linear Time ◽  
Theta Functions ◽  
Speed Up ◽  
Genus Two ◽  
The One ◽  
Time Borrowing ◽  
Genus One ◽  
Large Speed

We outline an algorithm to compute $\unicode[STIX]{x1D703}(z,\unicode[STIX]{x1D70F})$ in genus two in quasi-linear time, borrowing ideas from the algorithm for theta constants and the one for $\unicode[STIX]{x1D703}(z,\unicode[STIX]{x1D70F})$ in genus one. Our implementation shows a large speed-up for precisions as low as a few thousand decimal digits. We also lay out a strategy to generalize this algorithm to genus $g$.

NEUTRON–PROTON PAIRING CORRELATION FOR THE ROTATIONAL MOTION OF N = Z72Kr, 76Sr, AND 80Zr NUCLEI

2011 ◽  
Vol 20 (08) ◽  
pp. 1687-1699
Author(s):  
PRIANKA ROY ◽  
SHASHI K. DHIMAN
Keyword(s):  
Effective Interaction ◽  
Mean Field ◽  
High Spin State ◽  
Pairing Correlation ◽  
Effective Interactions ◽  
Hartree Fock ◽  
Self Consistent ◽  
The Mean ◽  
Proton Pairing ◽  
Band Crossing

The high-spin state properties of the neutron–proton (np) residual effective interaction are analyzed in N = Z72 Kr , 76 Sr , and 80 Zr nuclei. The self-consistent microscopic Hartree–Fock–Bogoliubov (HFB) equations have been solved by employing monopole corrected two-body effective interaction. A band crossing is observed in 72 Kr nucleus at J = 14ℏ state with monopole corrected "HPU1" and "HPU2" effective interactions. The VAP–HFB theory suggests that the "4p–4h" excitations by np residual interaction are the essential ingredients of the mean-field description of the occurence of backbending in 72 Kr nucleus.

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