Holographic three-point correlators in the Schrodinger/dipole CFT correspondence

We calculate, for the first time, three-point correlation functions involving "heavy" operators in the Schrodinger/null-dipole CFT correspondence at strong coupling. In particular, we focus on the three-point functions of the dilaton modes and two "heavy" operators. The heavy states are dual to the single spin and dyonic magnon, the single spin and dyonic spike solutions or to two novel string solutions which do not have an undeformed counterpart. Our results provide the leading term of the correlators in the large $\lambda$ expansion and are in perfect agreement with the form of the correlator dictated by non-relativistic conformal invariance. We also specify the scaling function which can not be fixed by using conformal invariance.Comment: 26 pages, 1 figur

Giant magnons and spiky strings in the Schrodinger/dipole-deformed CFT correspondence

We construct semi-classical string solutions of the Schr\"odinger $Sch_5 \times S^5$ spacetime, which is conjectured to be the gravity dual of a non-local dipole-deformed CFT. They are the counterparts of the giant magnon and spiky string solutions of the undeformed $AdS_5 \times S^5$ to which they flow when the deformation parameter is turned off. They live in an $S^3$ subspace of the five-sphere along the directions of which the $B$-field has non-zero components having also extent in the $Sch_5$ part of the metric. Finally, we speculate on the form of the dual field theory operators.Comment: 16 pages; v2: references adde

Measurement of the charm contribution to the proton structure function at HERA

We have measured the D*± production in deep inelastic scattering via the mode D*± —> D°irf-, D° -> K:fn^:TT±'n±, from positron-proton collisions at HERA, at a centre of mass energy of 300 GeV. For this purpose we have used data corresponding to an integrated luminosity of 6.62 pb~l collected in 1995 by the ZEUS detector. We measured the cross section for D* production to be cr(ep —>■ D*± + X) = (12.6 ± lAstat -nLys ^ 0^br)^ in the restricted kinematical region 1.5 < Pt{D*) < 15GeV/c, \r](D*)\ < 1.5, 1 < Q2 < 600GeV2 and 0.02 < y < 0.7. We have extracted the charm structure function Ef in bins of Bjorken x and Q2 by extrapolating the measured region of the phase space to the whole, using the RAPGAP event generator that simulates D* production in DIS via the boson-gluon fusion process. The F2C measurement was found to be in agreement with theoretical models using fixed or variable active flavour number to predict FI

Holographic three-point correlators at finite density and temperature

We calculate holographically three-point functions of scalar operators with large dimensions at finite density and finite temperature. To achieve this, we construct new solutions that involve two isometries of the deformed internal space. The novel feature of these solutions is that the corresponding two-point function depends not only on the conformal dimension but also on the difference between the two angular momenta. After identifying the dual operators, we systematically calculate three-point correlators as an expansion in powers of the temperature and the chemical potential. Our analytic perturbative results are in agreement with the exact numerical computation. The three point correlator (when the background contains either temperature or density but not both) is always a monotonic function of the temperature or the chemical potential. However, when both parameters are present the three point correlator is no longer a monotonic function. For fixed finite temperature and small values of the chemical potential a minimum of the three-point function appears. Surprisingly, contributions from the internal space do not depend on the chemical potential or the temperature, as long as those are treated as perturbations.Comment: 36 pages, 5 figure

Holographic correlation functions at finite density and/or finite temperature

We calculate holographically one and two-point functions of scalar operators at finite density and/or finite temperature. In the case of finite density and zero temperature we argue that only scalar operators can have non-zero VEVs. In the case in which both the chemical potential and the temperature are finite, we present a systematic expansion of the two-point correlators in powers of the temperature T and the chemical potential $\Omega$. The holographic result is in agreement with the general form of the OPE which dictates that the two-point function may be written as a linear combination of the Gegenbauer polynomials $C_J^{(1)}(\xi)$ but with the coefficients depending now on both the temperature and the chemical potential, as well as on the CFT data. The leading terms in this expansion originate from the expectation values of the scalar operator $\phi^2$, the R-current ${\cal J}^\mu_{\phi_3}$ and the energy-momentum tensor $T^{\mu\nu}$. By employing the Ward identity for the R-current and by comparing the appropriate term of the holographic result for the two-point correlator to the corresponding term in the OPE, we derive the value of the R-charge density of the background. Compelling agreement with the analysis of the thermodynamics of the black hole is found. Finally, we determine the behaviour of the two-point correlators, in the case of finite temperature, and in the limit of large temporal or spatial distance of the operators.Comment: 1+31 page

Index boundedness and uniform connectedness of space of the G-permutation degree

[EN] In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that: (1) If (X, U) is a uniform space, then the mapping π s n, G : (X n , U n ) → (SP n GX, SP n GU) is uniformly continuous and uniformly open, moreover w (U) = w (SP n GU); (2) If the mapping f : (X, U) → (Y, V) is a uniformly continuous (open), then the mapping SP n Gf : (SP n GX, SP n GU) → (SP n GY, SP n GV) is also uniformly continuous (open); (3) If the uniform space (X, U) is uniformly connected, then the uniform space (SP n GX, SP n GU) is also uniformly connected.Beshimov, RB.; Georgiou, DN.; Zhuraev, RM. (2021). Index boundedness and uniform connectedness of space of the G-permutation degree. Applied General Topology. 22(2):447-459. https://doi.org/10.4995/agt.2021.15566OJS447459222T. Banakh, Topological spaces with ith an ωω-base, Dissertationes Mathematicae, Warszawa, 2019. https://doi.org/10.4064/dm762-4-2018R. B. Beshimov, Nonincrease of density and weak density under weakly normal functors, Mathematical Notes 84 (2008), 493-497. https://doi.org/10.1134/S0001434608090216R. B. Beshimov, Some properties of the functor Oβ, Journal of Mathematical Sciences 133, no. 5 (2006), 1599-1601. https://doi.org/10.1007/s10958-006-0070-5R. B. Beshimov and N. K. Mamadaliev, Categorical and topological properties of the functor of Radon functionals, Topology and its Applications 275 (2020), 1-11. https://doi.org/10.1016/j.topol.2019.106998R. B. Beshimov and N. K. Mamadaliev, On the functor of semiadditive τ-smooth functionals, Topology and its Applications 221, no. 3 (2017), 167-177. https://doi.org/10.1016/j.topol.2017.02.037R. B. Beshimov, N. K. Mamadaliev, Sh. Kh. Eshtemirova, Categorical and cardinal properties of hyperspaces with a finite number of components, Journal of Mathematical Sciences 245, no. 3 (2020), 390-397. https://doi.org/10.1007/s10958-020-04701-8R. B. Beshimov and R. M. Zhuraev, Some properties of a connected topological group, Mathematics and Statistics 7, no. 2 (2019), 45-49. https://doi.org/10.13189/ms.2019.070203A. A. Borubaev and A. A. Chekeev, On completions of topological groups with respect to the maximal uniform structure and factorization of uniform homomorphisms with respect to uniform weight and dimension, Topology and its Applications 107, no. 1-2 (2000), 25-37. https://doi.org/10.1016/S0166-8641(99)00120-0A. A. Borubaev and A. A. Chekeev, On uniform topology and its applications, TWMS J. Pure and Appl. Math. 6, no. 2 (2015), 165-179.R. Engelking, General topology, Berlin: Helderman, 1986.V. V. Fedorchuk, Covariant functors in the category of compacts, absolute ute retracts and Q-manifolds, Uspekhi Matematicheskikh Nauk 36, no. 3 (1981), 177-195. https://doi.org/10.1070/RM1981v036n03ABEH004251V. V. Fedorchuk and H. A. Kunzi, Uniformly open mappings and uniform embeddings of function spaces, Topology and its Applications 61 (1995), 61-84. https://doi.org/10.1016/0166-8641(94)00023-VV. V. Fedorchuk and V. V. Filippov, Topology of hyperspaces and its applications, 4 Mathematica, cybernetica, Moscow, 48 p., 1989 (in Russian).G. Itzkowitz, S. Rothman, H. Strassberg and T. S. Wu, Characterization of equivalent uniformities in topological groups, Topology and its Applications 47 (1992), 9-34. https://doi.org/10.1016/0166-8641(92)90112-DI. M. James, Introduction to Uniform Spaces, London Mathematical Society, Lecture Notes Series 144, Cambridge University Press, Cambridge, 1990.J. L. Kelley, General Topology, Van Nostrand Reinhold, Princeton, NJ, 1955.L. Holá and L. D. R. Kocinac, Uniform boundedness in function spaces, Topology and its Applications 241 (2018), 242-251. https://doi.org/10.1016/j.topol.2018.04.006E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182. https://doi.org/10.1090/S0002-9947-1951-0042109-4T. N. Radul, On the functor of order-preserving functionals, Comment. Math. Univ. Carol. 39, no. 3 (1998), 609-615.T. K. Yuldashev and F. G. Mukhamadiev, The local density and the local weak density in the space of permutation degree and in Hattorri space, URAL Mathematical Journal 6, no. 2 (2020), 108-126. https://doi.org/10.15826/umj.2020.2.01