Mishnyakov Victor

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  PhD Student

I'm interested in knot theory, matrix models, AdS/CFT correspondence and other string theory topics. In knot theory, I was involved in the study of quantum invariants of knots and the properties of their perturbative decomposition.

Now I am interested in the phenomenon of superintegrability of matrix models and its various deformations. This phenomenon consists in the fact that the average in the matrix model from the correctly chosen characters is again expressed in terms of the characters calculated at special points. The method that we have developed while studying this phenomenon allows us to prove beautiful formulas for averages in matrix models in cases where other usual methods do not work. I am also involved in the application of matrix models to the description of various modes of quantum gravity, such as, for example, JT gravity.

In addition, I am engaged in other projects: the study of operator expansion in N=4 supersymmetric Yang-Mills theory in the presence of vacuum condensates, and localization calculations in two-dimensional supersymmetric sigma models.

Selected Publications:

1. Mironov, A., Mironov, S., Mishnyakov, V., Morozov, A., & Sleptsov, A. (2018). Coloured Alexander polynomials and KP hierarchy. Physics Letters B, 783, 268-273. arXiv: 1805.02761 [hep-th]
2. Mironov, A., V. Mishnyakov, and A. Morozov. "Non-Abelian W-representation for GKM." Physics Letters B 823 (2021): 136721. arXiv: 2107.02210 [hep-th]

Publications affiliated with ITMP:

1. Mironov, A.; Mishnyakov, V.; Morozov, A. (2023). "Tau-functions beyond the group elements". arXiv: 2312.00695 [hep-th].

2. Chan, C.-T.; Mishnyakov, V.; Popolitov, A.; Tsybikov, K. (2023). "On bilinear superintegrability for monomial matrix models in pure phase". arXiv: 2310.02639 [hep-th].

3. Mironov, A.; Mishnyakov, V.; Morozov, A.; Popolitov, A. (2023). "Commutative families in W∞�∞, integrable many-body systems and hypergeometric τ�-functions". arXiv: 2306.06623 [hep-th].

4. Mironov, A.; Mishnyakov, V.; Morozov, A.; Popolitov, A. (2023). "Commutative subalgebras from Serre relations". Physics Letters B. 845 (2023) 138122. arXiv: 2307.01048 [hep-th]. doi: 10.1016/j.physletb.2023.138122.

5. Mishnyakov, V.; Morozov, A.; Suprun, P. (2023). "Position Space Equations for Banana Feynman Diagrams". Nuclear Physics B. 992 (2023) 116245. arXiv: 2303.08851 [hep-th]. doi: 10.1016/j.nuclphysb.2023.116245. 

6. Kazakov, V.; Levkovich-Maslyuk, F.; Mishnyakov, V. (2023). "Integrable Feynman Graphs and Yangian Symmetry on the Loom". arXiv: 2304.04654 [hep-th].

7. Alekseev, V.; Festuccia, G.; Mishnyakov, V.; Terziev, N.; Zabzine, M. (2022). "Localizing non-linear N=(2,2) sigma model on S2". The European Physical Journal C. 766 (2022). arXiv: 2202.10501 [hep-th]. doi: 10.1140/epjc/s10052-022-10610-8.

8. Mishnyakov. V.; Oreshina, A. (2022). "Superintegrability in ββ-deformed Gaussian Hermitian matrix model from WW-operators". The European Physical Journal C. 82 (2022) 6, 548. arXiv: 2203.15675 [hep-th]. doi: 10.1140/epjc/s10052-022-10466-y.

9. Gorsky, A.; Kazakov, V.; Levkovich-Maslyuk, F.; Mishnyakov, V. (2022). "A Flow in the Forest". Journal of High Energy Physics. 03 (2023) 067. arXiv: 2210.07176 [hep-th]. doi: 10.1007/JHEP03(2023)067.

All publications