368
18 Momentum-Space SFT
properties of string theory shared by local QFTs: Cutkosky rules [6, 7], unitarity [9,10], analyticity in a subset of the primitive domain and crossing symmetry [3].
Finally, general soft theorems for string theory (and, in fact, any theory of quantum
gravity) have been proven in [2, 5, 12, 13]. All together, these properties establish
string theory as a very strong candidate for a consistent theory of everything. The
next main question is how to obtain an expression of SFT that is amenable to
explicit computations. This will certainly require to understand even better the deep
structure of SFT, a goal that this book will hopefully help the reader to achieve.
18.3 Suggested Readings
• SFT momentum-space action [4, 6, 14].
• Consistency properties of string theory [4]:
– generalized Wick rotation, Cutkosky rules and unitarity [6–11].
– analyticity and crossing symmetry [3].
– soft theorems [2, 5, 12, 13].
References
1. T. Bautista, A. Dabholkar, H. Erbin, Quantum gravity from timelike Liouville theory. J.
High Energy Phys. 2019(10), 284 (2019). https://doi.org/10.1007/JHEP10(2019)284. arXiv:
1905.12689
2. S. Chakrabarti, S.P. Kashyap, B. Sahoo, A. Sen, M. Verma, Subleading soft theorem
for multiple soft gravitons. J. High Energy Phys. 2017(12) (2017). https://doi.org/10.1007/
JHEP12(2017)150. arXiv: 1707.06803
3. C. de Lacroix, H. Erbin, A. Sen, Analyticity and crossing symmetry of super-string loop amplitudes. J. High Energy Phys. 2019(5), 139 (2019). https://doi.org/10.1007/JHEP05(2019)139.
arXiv: 1810.07197
4. C. de Lacroix, H. Erbin, S.P. Kashyap, A. Sen, M. Verma, Closed super-string field theory
and its applications. Int. J. Mod. Phys. A 32(28–29), 1730021 (2017). https://doi.org/10.1142/
S0217751X17300216. arXiv: 1703.06410
5. A. Laddha, A. Sen, Sub-subleading soft graviton theorem in generic theories of quantum gravity.
J. High Energy Phys. 2017(10), 065 (2017). https://doi.org/10.1007/JHEP10(2017)065. arXiv:
1706.00759
6. R. Pius, A. Sen, Cutkosky rules for superstring field theory. J. High Energy Phys. 2016(10)
(2016). https://doi.org/10.1007/JHEP10(2016)024. arXiv: 1604.01783
7. R. Pius, A. Sen, Unitarity of the box diagram. J. High Energy Phys. 2018(11), 094 (2018).
https://doi.org/10.1007/JHEP11(2018)094. arXiv: 1805.00984
8. A. Sen, One loop mass renormalization of unstable particles in superstring theory. J. High
Energy Phys. 2016(11) (2016). https://doi.org/10.1007/JHEP11(2016)050. arXiv: 1607.06500
9. A. Sen, Reality of superstring field theory action. J. High Energy Phys. 2016(11), 014 (2016).
https://doi.org/10.1007/JHEP11(2016)014. arXiv: 1606.03455
10. A. Sen, Unitarity of superstring field theory. J. High Energy Phys. 2016(12) (2016). https://doi.
org/10.1007/JHEP12(2016)115. arXiv: 1607.08244
11. A. Sen, Equivalence of two contour prescriptions in superstring perturbation theory. J. High
Energy Phys. 2017(04) (2017). https://doi.org/10.1007/JHEP04(2017)025. arXiv: 1610.00443
12. A. Sen, Soft theorems in superstring theory. J. High Energy Phys. 2017(06) (2017). https://doi.
org/10.1007/JHEP06(2017)113. arXiv: 1702.03934
18 Momentum-Space SFT
properties of string theory shared by local QFTs: Cutkosky rules [6, 7], unitarity [9,10], analyticity in a subset of the primitive domain and crossing symmetry [3].
Finally, general soft theorems for string theory (and, in fact, any theory of quantum
gravity) have been proven in [2, 5, 12, 13]. All together, these properties establish
string theory as a very strong candidate for a consistent theory of everything. The
next main question is how to obtain an expression of SFT that is amenable to
explicit computations. This will certainly require to understand even better the deep
structure of SFT, a goal that this book will hopefully help the reader to achieve.
18.3 Suggested Readings
• SFT momentum-space action [4, 6, 14].
• Consistency properties of string theory [4]:
– generalized Wick rotation, Cutkosky rules and unitarity [6–11].
– analyticity and crossing symmetry [3].
– soft theorems [2, 5, 12, 13].
References
1. T. Bautista, A. Dabholkar, H. Erbin, Quantum gravity from timelike Liouville theory. J.
High Energy Phys. 2019(10), 284 (2019). https://doi.org/10.1007/JHEP10(2019)284. arXiv:
1905.12689
2. S. Chakrabarti, S.P. Kashyap, B. Sahoo, A. Sen, M. Verma, Subleading soft theorem
for multiple soft gravitons. J. High Energy Phys. 2017(12) (2017). https://doi.org/10.1007/
JHEP12(2017)150. arXiv: 1707.06803
3. C. de Lacroix, H. Erbin, A. Sen, Analyticity and crossing symmetry of super-string loop amplitudes. J. High Energy Phys. 2019(5), 139 (2019). https://doi.org/10.1007/JHEP05(2019)139.
arXiv: 1810.07197
4. C. de Lacroix, H. Erbin, S.P. Kashyap, A. Sen, M. Verma, Closed super-string field theory
and its applications. Int. J. Mod. Phys. A 32(28–29), 1730021 (2017). https://doi.org/10.1142/
S0217751X17300216. arXiv: 1703.06410
5. A. Laddha, A. Sen, Sub-subleading soft graviton theorem in generic theories of quantum gravity.
J. High Energy Phys. 2017(10), 065 (2017). https://doi.org/10.1007/JHEP10(2017)065. arXiv:
1706.00759
6. R. Pius, A. Sen, Cutkosky rules for superstring field theory. J. High Energy Phys. 2016(10)
(2016). https://doi.org/10.1007/JHEP10(2016)024. arXiv: 1604.01783
7. R. Pius, A. Sen, Unitarity of the box diagram. J. High Energy Phys. 2018(11), 094 (2018).
https://doi.org/10.1007/JHEP11(2018)094. arXiv: 1805.00984
8. A. Sen, One loop mass renormalization of unstable particles in superstring theory. J. High
Energy Phys. 2016(11) (2016). https://doi.org/10.1007/JHEP11(2016)050. arXiv: 1607.06500
9. A. Sen, Reality of superstring field theory action. J. High Energy Phys. 2016(11), 014 (2016).
https://doi.org/10.1007/JHEP11(2016)014. arXiv: 1606.03455
10. A. Sen, Unitarity of superstring field theory. J. High Energy Phys. 2016(12) (2016). https://doi.
org/10.1007/JHEP12(2016)115. arXiv: 1607.08244
11. A. Sen, Equivalence of two contour prescriptions in superstring perturbation theory. J. High
Energy Phys. 2017(04) (2017). https://doi.org/10.1007/JHEP04(2017)025. arXiv: 1610.00443
12. A. Sen, Soft theorems in superstring theory. J. High Energy Phys. 2017(06) (2017). https://doi.
org/10.1007/JHEP06(2017)113. arXiv: 1702.03934