Monodromy relations from twisted homology

Casali, Eduardo; Mizera, Sebastian; Tourkine, Piotr

doi:10.1007/JHEP12(2019)087

Title: Monodromy relations from twisted homology

Abstract

We reformulate the monodromy relations of open-string scattering amplitudes as boundary terms of twisted homologies on the configuration spaces of Riemann surfaces of arbitrary genus. This allows us to write explicit linear relations involving loop integrands of open-string theories for any number of external particles and, for the first time, to arbitrary genus. In the non-planar sector, these relations contain seemingly unphysical contributions, which we argue clarify mismatches in previous literature. The text is mostly self-contained and presents a concise introduction to twisted homologies. As a result of this powerful formulation, we can propose estimates on the number of independent loop integrands based on Euler characteristics of the relevant configuration spaces, leading to a higher-genus generalization of the famous (n - 3)! result at genus zero.

Authors:

^[1]; Mizera, Sebastian ^[2]; Tourkine, Piotr ^[3]

Univ. of California, Davis, CA (United States)
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of Waterloo, ON (Canada); Inst. for Advanced Study, Princeton, NJ (United States)
Sorbonne Univ., Paris (France)

Publication Date:: 2019-12-11

Research Org.:: Univ. of California, Davis, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1597622

Grant/Contract Number:: SC0009999

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 12; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Casali, Eduardo, Mizera, Sebastian, and Tourkine, Piotr. Monodromy relations from twisted homology.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP12(2019)087.

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                    Casali, Eduardo, Mizera, Sebastian, & Tourkine, Piotr. Monodromy relations from twisted homology.  United States.  https://doi.org/10.1007/JHEP12(2019)087

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                    Casali, Eduardo, Mizera, Sebastian, and Tourkine, Piotr. Wed .  
"Monodromy relations from twisted homology".  United States.  https://doi.org/10.1007/JHEP12(2019)087.  https://www.osti.gov/servlets/purl/1597622.

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@article{osti_1597622,

  title        = {Monodromy relations from twisted homology},

  author       = {Casali, Eduardo and Mizera, Sebastian and Tourkine, Piotr},

  abstractNote = {We reformulate the monodromy relations of open-string scattering amplitudes as boundary terms of twisted homologies on the configuration spaces of Riemann surfaces of arbitrary genus. This allows us to write explicit linear relations involving loop integrands of open-string theories for any number of external particles and, for the first time, to arbitrary genus. In the non-planar sector, these relations contain seemingly unphysical contributions, which we argue clarify mismatches in previous literature. The text is mostly self-contained and presents a concise introduction to twisted homologies. As a result of this powerful formulation, we can propose estimates on the number of independent loop integrands based on Euler characteristics of the relevant configuration spaces, leading to a higher-genus generalization of the famous (n - 3)! result at genus zero.},

  doi          = {10.1007/JHEP12(2019)087},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 12,

  volume       = 2019,

  place        = {United States},

  year         = {2019},

  month        = {12}

}

Copy to clipboard

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Works referenced in this record:

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Works referencing / citing this record:

All-order differential equations for one-loop closed-string integrals and modular graph forms
journal, January 2020

Gerken, Jan E.; Kleinschmidt, Axel; Schlotterer, Oliver
Journal of High Energy Physics, Vol. 2020, Issue 1
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All-order differential equations for one-loop closed-string integrals and modular graph forms
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Title: Monodromy relations from twisted homology

Abstract

Citation Formats

Combinatorics and topology of Kawai-Lewellen-Tye relations journal, August 2017

Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers conference, February 2020

Feynman amplitudes and limits of heights journal, October 2016

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy journal, July 2017

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Symmetry properties of dual tree-graphN-point amplitudes journal, April 1970

Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts journal, March 2012

Feynman integrals and intersection theory journal, February 2019

On the Complex Selberg Integral journal, January 1987

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Vector Space of Feynman Integrals and Multivariate Intersection Numbers journal, November 2019

Monodromy and Jacobi-like relations for color-ordered amplitudes journal, June 2010

Tropical Amplitudes journal, February 2017

Tropical Amplitudes text, January 2017

Intersection Theory for Twisted Cycles journal, January 1994

Decomposition of Feynman integrals on the maximal cut by intersection numbers journal, May 2019

Monodromy relations in higher-loop string amplitudes journal, December 2017

Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes journal, May 2017

From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop journal, January 2019

Relations of loop partial amplitudes in gauge theory by Unitarity cut method journal, January 2012

Perturbative Quantum Gravity as a Double Copy of Gauge Theory journal, August 2010

Scattering Amplitudes from Intersection Theory journal, April 2018

Homology With Local Coefficients journal, October 1943

One-loop monodromy relations on single cuts journal, October 2017

A relation between tree amplitudes of closed and open strings journal, May 1986

Monodromy of hypergeometric functions and non-lattice integral monodromy journal, December 1986

The Feynman iε in string theory journal, April 2015

Multigluon cross sections and 5-jet production at hadron colliders journal, January 1989

Multiloop calculations in covariant superstring theory journal, June 1987

On general BCJ relation at one-loop level in Yang-Mills theory journal, January 2013

On vanishing of cohomology attached to certain many valued meromorphic functions journal, April 1975

Higher-Loop Amplitude Monodromy Relations in String and Gauge Theory journal, November 2016

Gauss-Manin connection of integral of difference products journal, April 1987

Intersection theory for twisted cohomologies and twisted Riemann’s period relations I journal, September 1995

Gauge amplitude identities by on-shell recursion relation in S-matrix program journal, January 2011

Elliptic Feynman integrals and pure functions journal, January 2019

Filling the gaps with PCO’s journal, September 2015

Minimal Basis for Gauge Theory Amplitudes journal, October 2009

The Euler characteristic of the moduli space of curves journal, October 1986

Double-Copy Structure of One-Loop Open-String Amplitudes journal, July 2018

Multiloop superstring amplitudes from non-minimal pure spinor formalism journal, December 2006

Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$ journal, January 2009

A contour integral representation for the dual five-point function and a symmetry of the genus-4 surface in journal, February 2006

Towards the n-point one-loop superstring amplitude. Part I. Pure spinors and superfield kinematics journal, August 2019

One-loop n-point gauge theory amplitudes, unitarity and collinear limits journal, August 1994

Minimal Basis for Gauge Theory Amplitudes text, January 2009

Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes text, January 2010

Relations of loop partial amplitudes in gauge theory by Unitarity cut method text, January 2011

Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts text, January 2011

On General BCJ Relation at One-loop Level in Yang-Mills Theory text, January 2012

Supermoduli Space Is Not Projected preprint, January 2013

The physics and the mixed Hodge structure of Feynman integrals preprint, January 2014

Feynman Amplitudes and Limits of Heights text, January 2015

Higher-loop amplitude monodromy relations in string and gauge theory text, January 2016

Monodromy Relations in Higher-Loop String Amplitudes text, January 2017

Combinatorics and Topology of Kawai-Lewellen-Tye Relations text, January 2017

Scattering Amplitudes from Intersection Theory text, January 2017

Feynman Integrals and Intersection Theory text, January 2018

Vector Space of Feynman Integrals and Multivariate Intersection Numbers text, January 2019

All-order differential equations for one-loop closed-string integrals and modular graph forms journal, January 2020

All-order differential equations for one-loop closed-string integrals and modular graph forms text, January 2019

Combinatorics and topology of Kawai-Lewellen-Tye relations
journal, August 2017

Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
conference, February 2020

Feynman amplitudes and limits of heights
journal, October 2016

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy
journal, July 2017

Super-Poincare covariant quantization of the superstring
journal, March 2000

The geometry of string perturbation theory
journal, October 1988

Symmetry properties of dual tree-graphN-point amplitudes
journal, April 1970

Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts
journal, March 2012

Feynman integrals and intersection theory
journal, February 2019

On the Complex Selberg Integral
journal, January 1987

Chiral bosonization, determinants and the string partition function
journal, January 1987

Conformal scalar fields and chiral splitting on super Riemann surfaces
journal, September 1989

Vector Space of Feynman Integrals and Multivariate Intersection Numbers
journal, November 2019

Monodromy and Jacobi-like relations for color-ordered amplitudes
journal, June 2010

Tropical Amplitudes
journal, February 2017

Tropical Amplitudes
text, January 2017

Intersection Theory for Twisted Cycles
journal, January 1994

Decomposition of Feynman integrals on the maximal cut by intersection numbers
journal, May 2019

Monodromy relations in higher-loop string amplitudes
journal, December 2017

Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes
journal, May 2017

From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
journal, January 2019

Relations of loop partial amplitudes in gauge theory by Unitarity cut method
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Perturbative Quantum Gravity as a Double Copy of Gauge Theory
journal, August 2010

Scattering Amplitudes from Intersection Theory
journal, April 2018

Homology With Local Coefficients
journal, October 1943

One-loop monodromy relations on single cuts
journal, October 2017

A relation between tree amplitudes of closed and open strings
journal, May 1986

Monodromy of hypergeometric functions and non-lattice integral monodromy
journal, December 1986

The Feynman iε in string theory
journal, April 2015

Multigluon cross sections and 5-jet production at hadron colliders
journal, January 1989

Multiloop calculations in covariant superstring theory
journal, June 1987

On general BCJ relation at one-loop level in Yang-Mills theory
journal, January 2013

On vanishing of cohomology attached to certain many valued meromorphic functions
journal, April 1975

Higher-Loop Amplitude Monodromy Relations in String and Gauge Theory
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Gauss-Manin connection of integral of difference products
journal, April 1987

Intersection theory for twisted cohomologies and twisted Riemann’s period relations I
journal, September 1995

Gauge amplitude identities by on-shell recursion relation in S-matrix program
journal, January 2011

Elliptic Feynman integrals and pure functions
journal, January 2019

Filling the gaps with PCO’s
journal, September 2015

Minimal Basis for Gauge Theory Amplitudes
journal, October 2009

The Euler characteristic of the moduli space of curves
journal, October 1986

Double-Copy Structure of One-Loop Open-String Amplitudes
journal, July 2018

Multiloop superstring amplitudes from non-minimal pure spinor formalism
journal, December 2006

Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$
journal, January 2009

A contour integral representation for the dual five-point function and a symmetry of the genus-4 surface in
journal, February 2006

Towards the n-point one-loop superstring amplitude. Part I. Pure spinors and superfield kinematics
journal, August 2019

One-loop n-point gauge theory amplitudes, unitarity and collinear limits
journal, August 1994

Minimal Basis for Gauge Theory Amplitudes
text, January 2009

Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
text, January 2010

Relations of loop partial amplitudes in gauge theory by Unitarity cut method
text, January 2011

Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts
text, January 2011

On General BCJ Relation at One-loop Level in Yang-Mills Theory
text, January 2012

Supermoduli Space Is Not Projected
preprint, January 2013

The physics and the mixed Hodge structure of Feynman integrals
preprint, January 2014

Feynman Amplitudes and Limits of Heights
text, January 2015

Higher-loop amplitude monodromy relations in string and gauge theory
text, January 2016

Monodromy Relations in Higher-Loop String Amplitudes
text, January 2017

Combinatorics and Topology of Kawai-Lewellen-Tye Relations
text, January 2017

Scattering Amplitudes from Intersection Theory
text, January 2017

Feynman Integrals and Intersection Theory
text, January 2018

Vector Space of Feynman Integrals and Multivariate Intersection Numbers
text, January 2019

All-order differential equations for one-loop closed-string integrals and modular graph forms
journal, January 2020

All-order differential equations for one-loop closed-string integrals and modular graph forms
text, January 2019