On the massless tree-level S-matrix in 2d sigma models

@article{Hoare2019OnTM,
  title={On the massless tree-level S-matrix in 2d sigma models},
  author={Ben Hoare and Nat Levine and Arkady A. Tseytlin},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2019},
  volume={52}
}
Motivated by the search for new integrable string models, we study the properties of massless tree-level S-matrices for 2d -models expanded near the trivial vacuum. We find that, in contrast to the standard massive case, there is no apparent link between massless S-matrices and integrability: in well-known integrable models the tree-level massless S-matrix fails to factorize and exhibits particle production. Such tree-level particle production is found in several classically integrable models… 

Figures and Tables from this paper

Tree level integrability in 2d quantum field theories and affine Toda models
We investigate the perturbative integrability of massive (1+1)-dimensional bosonic quantum field theories, focusing on the conditions for them to have a purely elastic S-matrix, with no particle
Geometry of massless scattering in integrable superstring
A bstractWe consider the action of the q-deformed Poincaré superalgebra on the massless non-relativistic R-matrix in ordinary (undeformed) integrable AdS2 × S2 × T6 type IIB superstring theory. The
Boundary correlators in WZW model on AdS2
Boundary correlators of elementary fields in some 2d conformal field theories defined on AdS$_2$ have a particularly simple structure. For example, the correlators of the Liouville scalar happen to
A study of integrable form factors in massless relativistic AdS 3
  • A. Torrielli
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2022
We show that the massless integrable sector of the AdS 3 × S 3 × T 4 superstring theory, which admits a non-trivial relativistic limit, provides a setting where it is possible to determine exact
Analytic nonintegrability and S -matrix factorization
We formulate an equivalence between the 2-dim $\sigma$-model spectrum expanded on a non-trivial massive vacuum and a classical particle Hamiltonian with variable mass and potential. By considering
Free fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 satisfy the so-called free fermion
On the Hamiltonian formulation, integrability and algebraic structures of the Rajeev-Ranken model
The integrable 1+1-dimensional SU(2) principal chiral model (PCM) serves as a toy-model for 3+1-dimensional Yang-Mills theory as it is asymptotically free and displays a mass gap. Interestingly, the
Do Drinfeld twists of AdS 5 × S 5 survive light-cone quantization?
We study how a wide class of Abelian Yang-Baxter deformations of the AdS 5 × S 5 string behave at the quantum level. These deformations are equivalent to TsT transformations and conjectured to be
Do Drinfeld twists of $AdS_5 \times S^5$ survive light-cone quantization?
We study how a wide class of Abelian Yang-Baxter deformations of the AdS_5 \times S^5AdS5×S5 string behave at the quantum level. These deformations are equivalent to TsT transformations and
Norms and scalar products for AdS3
We compute scalar products and norms of Bethe vectors in the massless sector of AdS3 integrable superstring theories, by exploiting the general difference form of the S-matrix of massless excitations
...
...

References

SHOWING 1-10 OF 47 REFERENCES
Looking for integrability on the worldsheet of confining strings
A bstractWe study restrictions on scattering amplitudes on the worldvolume of branes and strings (such as confining flux tubes in QCD) implied by the target space Poincaré symmetry. We focus on
Worldsheet scattering in AdS(5) x S**5
We calculate the S-matrix in the gauge-fixed sigma-model on AdS(5) x S-5 to the leading order in perturbation theory, and analyze how supersymmetry is realized on the scattering states. A mild
S-Matrix equivalence theorem evasion and dimensional regularisation with the canonical MHV lagrangian
We demonstrate that the canonical change of variables that yields the MHV lagrangian, also provides contributions to scattering amplitudes that evade the equivalence theorem. This 'ET evasion' in
On T-duality and integrability for strings on AdS backgrounds
We discuss an interplay between T-duality and integrability for certain classical non-linear sigma models. In particular, we consider strings on the AdS5 ? S5 background and perform T-duality along
A class of exact pp-wave string models with interacting light-cone gauge actions
We find a general class of pp-wave string solutions with NS-NS $H_3$ or R-R $F_3$ field strengths, which are analogous to solutions with non-constant $F_5$ recently considered by Maldacena and Maoz
Beta function of k deformed AdS5 × S5 string theory
A bstractWe calculate the one loop beta function for the would-be marginal coupling on the world sheet of the k deformed sigma models associated to a quantum group with q = eiπ/k. This includes the
Strings on pp-waves and massive two-dimensional field theories
Abstract We find a general class of pp-wave solutions of type IIB string theory such that the light cone gauge worldsheet Lagrangian is that of an interacting massive field theory. When the light
...
...