More three-point correlators of giant magnons with finite size. (English) Zbl 1298.81250
Summary: In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to heavy string states, while the third vertex corresponds to a light state. This is done for the case when the heavy string states are \(finite-size\) giant magnons with one or two angular momenta, and for two different choices of the light state, corresponding to dilaton operator and primary scalar operator. The relevant operators in the dual gauge theory are \( \mathrm{Tr}\left( {F_{\mu \nu }^2{Z^j} + \dots } \right) \) and \(\mathrm{Tr}(Z^{j})\). We first consider the case of \(\mathrm{AdS}_{5} {\times} S^{5}\) and \(\mathcal{N}=4 \) super Yang-Mills. Then we extend the obtained results to the \(\gamma\)-deformed \(\mathrm{AdS}_{5} {\times} S_{\gamma}^{5}\), dual to \(\mathcal{N}=1 \) super Yang-Mills theory, arising as an exactly marginal deformation of \(\mathcal{N}=4 \) super Yang-Mills.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 81T18 | Feynman diagrams |
| 81T60 | Supersymmetric field theories in quantum mechanics |
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