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Flat coordinates for Saito Frobenius manifolds and string theory
Theoretical and Mathematical Physics. 2016. Vol. 189. No. 3. P. 1775–1789.
Belavin A. A., Gepner D., Kononov Y.
We investigate the connection between the models of topological conformal theory and noncritical string theory with Saito Frobenius manifolds. For this, we propose a new direct way to calculate the flat coordinates using the integral representation for solutions of the Gauss–Manin system connected with a given Saito Frobenius manifold. We present explicit calculations in the case of a singularity of type An. We also discuss a possible generalization of our proposed approach to SU(N)k/(SU(N)k+1 × U(1)) Kazama–Suzuki theories. We prove a theorem that the potential connected with these models is an isolated singularity, which is a condition for the Frobenius manifold structure to emerge on its deformation manifold. This fact allows using the Dijkgraaf–Verlinde–Verlinde approach to solve similar Kazama–Suzuki models.
Merkulov S., Manin Y. I., Topological Methods in Nonlinear Analysis 1997 Vol. 9 No. 1 P. 107–161
Added: October 1, 2026
Merkulov S., International Mathematics Research Notices 1998 No. 14 P. 727–733
Added: October 1, 2026
Ievlev E., Marshakov A., Sumbatian G. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 114 Article 046006
We continue the study of non-Abelian vortex string in 4D N =2 supersymmetric QCD (SQCD) as
critical superstring, and extend this analysis to UðNÞ gauge theory with arbitrary even N and Nf = 2N
number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is
still given by the string spectrum on the ...
Added: August 13, 2026
Evgenii Ievlev, Andrei Marshakov, Sumbatian G. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2025 Vol. 112 No. 10 Article 105010
It has been shown that the non-Abelian vortex string in 4D N = 2 supersymmetric QCD (SQCD)
with the U(2) gauge group and N_f = 4 flavors becomes a critical superstring. Its 10D target space is a
product of the flat 4D space and an internal noncompact Calabi-Yau threefold, namely, the conifold. It was
also shown that the Coulomb branch ...
Added: December 2, 2025
E. Ievlev, Pichugina P., A. Yung, International Journal of Modern Physics A 2025 Vol. 40 No. 24 Article 2550091
It has been demonstrated that the non-Abelian solitonic vortex string in four-dimensional (4D) N=2 supersymmetric QCD (SQCD) with gauge group U(2) and Nf=4 quark hypermultiplets behaves as a critical superstring. This string propagates in a ten-dimensional space comprising the flat 4D space and an internal Calabi–Yau noncompact threefold, specifically, the conifold. The lowest state of this string is a ...
Added: October 2, 2025
Gavrilenko P., Evgenii Ievlev, Marshakov A. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2025 Vol. 111 No. 10 Article 106003
We consider a class of two dimensional conformal N = 2 supersymmetric U(1) gauge linear sigma
models with N fields of charges +1 and N fields of charges −1, whose Higgs branches are noncompact toric
Calabi-Yau manifolds of complex dimension 2N − 1. We show, starting from large-N approximation, that
the Coulomb branch of these models, which opens up at ...
Added: May 14, 2025
A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2024 Vol. 110 No. 2 Article 025004
It has been shown that non-Abelian solitonic vortex string supported in four-dimensional (4D) N = 2
supersymmetric QCD (SQCD) with the U(2) gauge group and Nf =4 quark flavors becomes a critical
superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space
and an internal space given by a Calabi-Yau noncompact threefold, ...
Added: September 20, 2024
A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2022 Vol. 106 No. 10 Article 106019
It has been shown that the non-Abelian solitonic vortex string supported in four-dimensional (4D)
N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and N_f = 4 quark flavors becomes a
critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D
space and an internal space given by a Calabi-Yau noncompact ...
Added: December 21, 2022
A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2021 Vol. 104 No. 2 Article 025007
It has been shown that non-Abelian solitonic vortex strings supported in four-dimensional (4D)
N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and N_f =4 quark flavors behave
as critical superstrings. In addition to four translational moduli, the non-Abelian strings under
consideration carry six orientational and size moduli. Together they form a ten-dimensional space
required for a superstring to ...
Added: October 26, 2022
E. Ievlev, A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2021 Vol. 104 No. 11 Article 114033
It has been shown that non-Abelian vortex string supported in four-dimensional (4D) N =2
supersymmetric QCD (SQCD) with the U(2) gauge group and N_f =4 quark flavors becomes a critical
superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space
and an internal space given by a Calabi-Yau noncompact threefold, namely, ...
Added: October 26, 2022
Basalaev A., Takahashi A., International Mathematics Research Notices 2022 Vol. 2022 No. 19 P. 14865–14922
For any triple of positive integers A′=(a′1,a′2,a′3) and c∈C∗, cusp polynomial fA′=xa′11+xa′22+xa′33−c−1x1x2x3 is known to be mirror to Geigle–Lenzing orbifold projective line P1a′1,a′2,a′3. More precisely, with a suitable choice of a primitive form, the Frobenius manifold of a cusp polynomial fA′ turns out to be isomorphic to the Frobenius manifold of the Gromov–Witten theory of ...
Added: September 9, 2022
Basalaev A., Dunin-Barkowski P., Natanzon S., Journal of Physics A: Mathematical and Theoretical 2021 Vol. 54 No. 11 P. 1–25
We propose a new construction of an integrable hierarchy associated to any infinite series of Frobenius manifolds satisfying a certain stabilization condition. We study these hierarchies for Frobenius manifolds associated to AN, DN and BN singularities. In the case of AN Frobenius manifolds our hierarchy turns out to coincide with the KP hierarchy; for BN ...
Added: March 19, 2021
Buryak A., Shadrin S., Letters in Mathematical Physics 2010 Vol. 93 No. 3 P. 243–252
In this note we use the formalism of multi-KP hierarchies in order to give some general formulas for infinitesimal deformations of solutions of the Darboux-Egoroff system. As an application, we explain how Shramchenko's deformations of Frobenius manifold structures on Hurwitz spaces fit into the general formalism of Givental-van de Leur twisted loop group action on ...
Added: October 5, 2020
Buryak A., Moscow Mathematical Journal 2020 Vol. 20 No. 3 P. 475–493
By a famous result of K. Saito, the parameter space of the miniversal deformation of the $A_{r-1}$-singularity carries a Frobenius manifold structure. The Landau-Ginzburg mirror symmetry says that, in the flat coordinates, the potential of this Frobenius manifold is equal to the generating series of certain integrals over the moduli space of $r$-spin curves. In ...
Added: May 22, 2020
Basalaev A., Buryak A., International Mathematics Research Notices 2021 Vol. 2021 No. 7 P. 5460–5491
A well-known construction of B. Dubrovin and K. Saito endows the parameter space of a universal unfolding of a simple singularity with a Frobenius manifold structure. In our paper, we present a generalization of this construction for the singularities of types A and D that gives a solution of the open WDVV equations. For the A-singularity, the resulting solution describes ...
Added: April 21, 2020
Ionov A., Journal of Geometry and Physics 2019 Vol. 140 P. 125–130
We provide a construction of Saito primitive forms for Gepner singularity by studying the relation between Saito primitive forms for Gepner singularities and primitive forms for singularities of the form F_{k,n} = ∑^n_{i=1} x^k_i invariant under the natural S_n-action. ...
Added: November 8, 2019
Losiakov V., Тютин И. В., Теоретическая и математическая физика 2019 Т. 199 № 1 С. 142–153
In the framework of general relativity theory, we consider a space-time whose metric depends on only one coordinate and time. We choose a gauge class such that all the constraint conditions of the theory of gravity as a gauge theory are explicitly solved and construct a Hamiltonian depending only on dynamical physical variables (gravitons). We ...
Added: October 31, 2019
Koile E., Kovensky N., Schvellinger M., Journal of High Energy Physics 2015 Vol. 2015 No. 12 P. 1–37
Differential cross sections of deep inelastic scattering of charged leptons from hadrons are investigated by using the gauge/string duality. We consider vector mesons derived from different holographic dual models obtaining a general expression. We focus on the strongly coupled regime of dual gauge theories for different values of the Bjorken parameter. We find new predictions ...
Added: October 31, 2019
Koile E., Kovensky N., Schvellinger M., Journal of High Energy Physics 2015 Vol. 2015 No. 1 P. 1–48
Deep inelastic scattering of leptons from hadrons at small values of the Bjorken parameter x is studied from superstring theory. In particular, we focus on single-flavored scalar and vector mesons in the large N limit. This is studied in terms of different holographic dual models with flavor Dp-branes in type IIA and type IIB superstring ...
Added: October 31, 2019
Koile E., Macaluso S., Schvellinger M., Journal of High Energy Physics 2014 Vol. 2014 No. 1 P. 166–206
Two-point current correlation functions of the large N limit of supersymmetric and non-supersymmetric Yang-Mills theories at strong coupling are investigated in terms of their string theory dual models with quenched flavors. We consider non-Abelian global symmetry currents, which allow one to investigate vector mesons with N f > 1. From the correlation functions we construct ...
Added: October 31, 2019
Koile E., Macaluso S., Schvellinger M., Journal of High Energy Physics 2012 Vol. 2012 No. 2 P. 103–139
We study deep inelastic scattering structure functions from hadrons using different holographic dual models which describe the strongly coupled regime of gauge theories in the large N limit. Particularly, we consider scalar and vector mesons obtained from holographic descriptions with fundamental degrees of freedom, corresponding to N = 2 supersymmetric and non-supersymmetric Yang-Mills theories. We ...
Added: October 31, 2019
Basalaev A., Journal of Geometry and Physics 2018 Vol. 2014 No. 84 P. 73–86
We study Frobenius manifolds of rank three and dimension one that are related to submanifolds of certain Frobenius manifolds arising in mirror symmetry of elliptic orbifolds. We classify such Frobenius manifolds that are defined over an arbitrary field K⊂C via the theory of modular forms. By an arithmetic property of an elliptic curve Eτ defined ...
Added: February 26, 2019