## On the exactness of soft theorems

## Abstract

Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. Moreover, as further evidence for the exactness of type (II) soft theorems, we consider the α' expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to $$\mathcal{O}$$ (α' ^{6}) . Thus the massless S-matrix of string theory “knows” about the presence of D-branes.

- Authors:

- ICTP South American Inst. for Fundamental Research, São Paulo (Brazil); Chulalongkorn Univ., Bangkok (Thailand); Istituto Nazionale di Fisica Nucleare (INFN), Rome (Italy)
- National Taiwan Univ., Taipei (Taiwan); National Tsing Hua Univ., Hsinchu (Taiwan)
- National Taiwan Univ., Taipei (Taiwan)
- California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of California, Los Angeles, CA (United States)

- Publication Date:

- Research Org.:
- California Inst. of Technology (CalTech), Pasadena, CA (United States)

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

- OSTI Identifier:
- 1501903

- Grant/Contract Number:
- SC0010255

- 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: 2017; Journal Issue: 12; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Scattering Amplitudes; Spontaneous Symmetry Breaking; Effective Field Theories; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Guerrieri, Andrea L., Huang, Yu-tin, Li, Zhizhong, and Wen, Congkao. On the exactness of soft theorems. United States: N. p., 2017.
Web. doi:10.1007/jhep12(2017)052.
```

```
Guerrieri, Andrea L., Huang, Yu-tin, Li, Zhizhong, & Wen, Congkao. On the exactness of soft theorems. United States. doi:10.1007/jhep12(2017)052.
```

```
Guerrieri, Andrea L., Huang, Yu-tin, Li, Zhizhong, and Wen, Congkao. Tue .
"On the exactness of soft theorems". United States. doi:10.1007/jhep12(2017)052. https://www.osti.gov/servlets/purl/1501903.
```

```
@article{osti_1501903,
```

title = {On the exactness of soft theorems},

author = {Guerrieri, Andrea L. and Huang, Yu-tin and Li, Zhizhong and Wen, Congkao},

abstractNote = {Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. Moreover, as further evidence for the exactness of type (II) soft theorems, we consider the α' expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to $\mathcal{O}$ (α'6) . Thus the massless S-matrix of string theory “knows” about the presence of D-branes.},

doi = {10.1007/jhep12(2017)052},

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

number = 12,

volume = 2017,

place = {United States},

year = {2017},

month = {12}

}