scholarly journals Two-loop superstring five-point amplitudes. Part I. Construction via chiral splitting and pure spinors

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Eric D’Hoker ◽  
Carlos R. Mafra ◽  
Boris Pioline ◽  
Oliver Schlotterer
Keyword(s):  
First Principles ◽  
Riemann Surfaces ◽  
Companion Paper ◽  
Type Ii ◽  
Pure Spinor ◽  
Perfect Agreement ◽  
Brst Cohomology ◽  
Spinor Formulation ◽  
Compact Riemann Surfaces ◽  
Genus Two

Abstract 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.

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 Two-loop superstring five-point amplitudes. Part III. Construction via the RNS formulation: even spin structures

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Eric D’Hoker ◽  
Oliver Schlotterer
Keyword(s):  
First Principles ◽  
Type Ii ◽  
Spin Structures ◽  
Genus Two

Abstract The contribution from even spin structures to the genus-two amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genus-two amplitude with four external NS states. The results agree with the parity-even NS components of a construction using chiral splitting and pure spinors given in earlier companion papers [29] and [33].

scholarly journals Advantage of the second-order formalism in double space T-dualization of type II superstring

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
B. Nikolić ◽  
B. Sazdović
Keyword(s):  
Order Theory ◽  
Type Ii ◽  
Pure Spinor ◽  
Superstring Theory ◽  
First Order ◽  
First Order Theory ◽  
Double Space ◽  
Spinor Formulation ◽  
Space Formalism ◽  
Background Fields

Abstract In this article we present bosonic T-dualization in double space of the type II superstring theory in the pure spinor formulation. We use the action with constant background fields obtained from the general case under some physically and mathematically justified assumptions. Unlike Nikolić and Sazdović (EPJ C 77:197, 2017), where we used the first-order theory, in this article fermionic momenta are integrated out. Full T-dualization in double space is represented as a permutation of the initial $$x^\mu $$xμ and T-dual coordinates $$y_\mu $$yμ. Requiring that a T-dual transformation law of the T-dual double coordinate $${}^\star Z^M=(y_\mu ,x^\mu )$$⋆ZM=(yμ,xμ) to be of the same form as for initial one $$Z^M=(x^\mu ,y_\mu )$$ZM=(xμ,yμ), we obtain the form of the T-dual background fields in terms of the initial ones. The advantage of using the action with integrated fermionic momenta is that it gives all T-dual background fields in terms of the initial ones. In the case of the first-order theory Nikolić and Sazdović (2017) a T-dual R-R field strength was obtained out of the double space formalism under additional assumptions.

A first-principles study on the electronic and optical properties of a type-II C2N/g-ZnO van der Waals heterostructure

2021 ◽  
Vol 23 (6) ◽  
pp. 3963-3973
Author(s):  
Jianxun Song ◽  
Hua Zheng ◽  
Minxia Liu ◽  
Geng Zhang ◽  
Dongxiong Ling ◽  
...  
Keyword(s):  
Optical Properties ◽  
Dft Calculations ◽  
First Principles ◽  
Van Der Waals ◽  
Band Alignment ◽  
Type Ii ◽  
Electronic And Optical Properties ◽  
Direct Bandgap ◽  
Van Der Waals Heterostructure ◽  
Vdw Heterostructure

The structural, electronic and optical properties of a new vdW heterostructure, C2N/g-ZnO, with an intrinsic type-II band alignment and a direct bandgap of 0.89 eV at the Γ point are extensively studied by DFT calculations.

A Hodge theoretic projective structure on compact Riemann surfaces

2021 ◽  
Vol 149 ◽  
pp. 1-27
Author(s):  
Indranil Biswas ◽  
Elisabetta Colombo ◽  
Paola Frediani ◽  
Gian Pietro Pirola
Keyword(s):  
Riemann Surfaces ◽  
Projective Structure ◽  
Compact Riemann Surfaces

scholarly journals Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

2021 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexander I. Bobenko ◽  
Ulrike Bücking
Keyword(s):  
Error Estimate ◽  
Branch Point ◽  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Convergence Result ◽  
Edge Length ◽  
Ramified Covering ◽  
Compact Riemann Surfaces ◽  
Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

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