Papers by Sergey Slizovskiy
Physical Review D Particles and Fields, 2006
In the finite-temperature Yang-Mills theory we calculate the functional determinant for fermions ... more In the finite-temperature Yang-Mills theory we calculate the functional determinant for fermions in the fundamental representation of the SU(N) gauge group in the background of an instanton with nontrivial holonomy at spatial infinity. This object, called the Kraan-van Baal-Lee-Lu caloron, can be viewed as composed of N Bogomolny-Prasad-Sommerfeld monopoles (or dyons). We compute analytically two leading terms of the fermionic determinant at large separations between dyons.
Jetp Lett Engl Tr, Jun 1, 2010
We present a geometric construction of 2D chiral boson theories on manifolds with tangent bundle ... more We present a geometric construction of 2D chiral boson theories on manifolds with tangent bundle admitting flat connection with possible torsion. The construction is based on embedding of the theory into the super-symmetric βγ - bc system. To perform the embedding we do a covariant smooth point-splitting of vector field observables and then the fermions are killed by a strongly oscillating chiral gauge transformation.
Physical Review Letters, Feb 13, 2015
We analyze the temperature and doping dependence of the specific heat C(T ) in NaxCoO2. This mate... more We analyze the temperature and doping dependence of the specific heat C(T ) in NaxCoO2. This material has a non-monotonic fermionic dispersion and is known to become magnetic at x ≥ 0.75. Before that, NaxCoO2 was conjectured to undergo a Lifshitz -type topological transition at x = xc = 0.62, in which a new electron Fermi pocket emerges at the Γ point, in addition to the existing hole pocket with large kF . The data [Y. Okamoto, A. Nishio, and Z. Hiroi, Phys. Rev. B 81, 12110(R) (2010)] show that near x = xc, the temperature dependence of C(T )/T at low T gets stronger as x approaches xc from below and then reverses the trend and changes sign at x ≥ xc. We argue that this behavior can be quantitatively explained within the spin-fluctuation theory. We show that magnetic fluctuations are enhanced near xc at momenta around kF and behave as weakly damped spin waves at x ≤ xc and as overdamped paramagnons at x > xc, when the new pocket forms. We demonstrate that this explains the temperature dependence of C(T )/T . At larger x the system enters a magnetic quantum critical regime where C(T )/T roughly scales as log T .
J Phys a Math Theor, 2009
Previously, it has been shown that in a spin-charge separated SU(2) Yang-Mills theory, (Euclidean... more Previously, it has been shown that in a spin-charge separated SU(2) Yang-Mills theory, (Euclidean) spacetime rotation invariance can be broken by an infinitesimal 1-cocycle that appears in the SO(4) boosts. Here we study in detail the structure of this 1-cocycle. In particular, we show that its non-triviality relates to the presence of a (Dirac) magnetic monopole bundle. We also compute the finite version of the cocycle.
Physical review letters, Jan 13, 2015
We analyze the temperature and doping dependence of the specific heat C(T) in Na_{x}CoO_{2}. This... more We analyze the temperature and doping dependence of the specific heat C(T) in Na_{x}CoO_{2}. This material was conjectured to undergo a Lifshitz-type topological transition at x=x_{c}=0.62, in which a new electron Fermi pocket emerges at the Γ point, in addition to the existing hole pocket with large k_{F}. The data show that near x=x_{c}, the temperature dependence of C(T)/T at low T gets stronger as x approaches x_{c} from below and then reverses the trend and changes sign at x≥x_{c}. We argue that this behavior can be quantitatively explained within the spin-fluctuation theory. We show that magnetic fluctuations are enhanced near x_{c} at momenta around k_{F}, and their dynamics changes between x≤x_{c} and x>x_{c}, when the new pocket forms. We demonstrate that this explains the temperature dependence of C(T)/T. We show that at larger x (x>0.65) the system enters a magnetic quantum critical regime where C(T)/T roughly scales as logT. This behavior extends to progressively l...
Physical Review D, 2004
We calculate exactly functional determinants for quantum oscillations about periodic instantons w... more We calculate exactly functional determinants for quantum oscillations about periodic instantons with non-trivial value of the Polyakov line at spatial infinity. Hence, we find the weight or the probability with which calorons with non-trivial holonomy occur in the Yang-Mills partition function. The weight depends on the value of the holonomy, the temperature, ΛQCD, and the separation between the BPS monopoles (or dyons) which constitute the periodic instanton. At large separation between constituent dyons, the quantum measure factorizes into a product of individual dyon measures, times a definite interaction energy. We present an argument that at temperatures below a critical one related to ΛQCD, trivial holonomy is unstable, and that calorons "ionize" into separate dyons.
Physical Review B, 2014
We study the Fermi surface topological transition of the pocket-opening type in a two dimensional... more We study the Fermi surface topological transition of the pocket-opening type in a two dimensional Fermi liquid. We find that the paramagnetic fluctuations in an interacting Fermi liquid typically drive the transition first order at zero temperature. We first gain insight from a calculation using second order perturbation theory in the self-energy. This is valid for weak interaction and far from instabilities. We then extend the results to stronger interaction, using the self-consistent fluctuation approximation. Experimental signatures are given in the light of these results.
Physical Review D, 2005
We calculate exactly the functional determinant for fermions in fundamental representation of SU ... more We calculate exactly the functional determinant for fermions in fundamental representation of SU (2) in the background of periodic instanton with non-trivial value of the Polyakov line at spatial infinity. The determinant depends on the value of the holonomy v, the temperature, and the parameter r12, which at large values can be treated as separation between the Bogomolny-Prasad-Sommerfeld monopoles (or dyons) which constitute the periodic instanton. We find a compact expression for small and large r12 and compute the determinant numerically for arbitrary r12 and v.
Physical Review D, 2006
In the finite-temperature Yang-Mills theory we calculate the functional determinant for fermions ... more In the finite-temperature Yang-Mills theory we calculate the functional determinant for fermions in the fundamental representation of SU (N ) gauge group in the background of an instanton with non-trivial holonomy at spatial infinity. This object, called the Kraan-van Baal -Lee-Lu caloron, can be viewed as composed of N Bogomolny-Prasad-Sommerfeld monopoles (or dyons). We compute analytically two leading terms of the fermionic determinant at large separations.
Physical Review B, 2012
We compute the magnetization of graphene in a magnetic field, taking into account for generality ... more We compute the magnetization of graphene in a magnetic field, taking into account for generality the possibility of a mass gap. We concentrate on the physical regime where quantum oscillations are not observed due to the effect of the temperature or disorder and show that the magnetization exhibits non-linear behaviour as a function of the applied field, reflecting the strong non-analyticity of the two-dimensional effective action of Dirac electrons. The necessary values of the magnetic field to observe this non-linearity vary from a few Teslas for very clean suspended samples to 20-30 Teslas for good samples on substrate. In the light of these calculations, we discuss the effects of disorder and interactions as well as the experimental conditions under which the predictions can be observed.
Journal of Physics A: Mathematical and Theoretical, 2009
Previously it has been shown that in spin-charge separated SU(2) Yang-Mills theory Lorentz invari... more Previously it has been shown that in spin-charge separated SU(2) Yang-Mills theory Lorentz invariance can become broken by a one-cocycle that appears in the Lorentz boosts. Here we study in detail the structure of this one-cocycle. In particular we show that its non-triviality relates to the presence of a (Dirac) magnetic monopole bundle. We also explicitely present the finite version of the cocycle.
Journal of Physics A: Mathematical and Theoretical, 2010
We are interested in a gauge invariant coupling between four dimensional Yang-Mills field and a t... more We are interested in a gauge invariant coupling between four dimensional Yang-Mills field and a three brane that can fluctuate into higher dimensions. For this we interpret the Yang-Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge field in a manner that displays the original gauge symmetry as an isometry. The brane moves in this higher dimensional space-time under the influence of its bulk gravity, with dynamics determined by the Nambu action. This introduces the desired interaction between the brane and the gauge field in a way that preserves the original gauge invariance as an isometry of the induced metric. After a prudent change of variables the result can be interpreted as a gauge invariant and massive vector field that propagates in the original space-time R 4 : The presence of the brane becomes entirely invisible, except for the mass.
Journal of Geometry and Physics, 2011
Instantonic theories are quantum field theories where all correlators are determined by integrals... more Instantonic theories are quantum field theories where all correlators are determined by integrals over the finite-dimensional space (space of generalized instantons). We consider novel geometrical observables in instantonic topological quantum mechanics that are strikingly different from standard evaluation observables. These observables allow jumps of special type of the trajectory (at the point of insertion of such observables). They do not (anti)commute with evaluation observables and raise the dimension of the space of allowed configurations, while the evaluation observables lower this dimension. We study these observables in geometric and operator formalisms. Simple examples are explicitly computed; they depend on linking of the points.
JETP Letters, 2010
We present a geometric construction of 2D chiral boson theories on manifolds with tangent bundle ... more We present a geometric construction of 2D chiral boson theories on manifolds with tangent bundle admitting at connection with possible torsion. The construction is based on embedding of the theory into the supersymmetric bc system. To perform the embedding we do a covariant smooth point-splitting of vector eld observables and then the fermions are killed by a strongly oscillating chiral gauge transformation.
We consider the coupling between four dimensional Yang-Mills field and a three brane that fluctua... more We consider the coupling between four dimensional Yang-Mills field and a three brane that fluctuates into higher dimensions. For this we interpret the Yang-Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge field in a manner that displays the original gauge symmetry
We inquire whether a resolution to the electroweak hierarchy problem could reside in symmetries t... more We inquire whether a resolution to the electroweak hierarchy problem could reside in symmetries that relate the bosonic Weinberg-Salam Lagrangian with a higher dimensional generally covariant theory. For this we consider a three-brane that moves under the influence of a seven dimensional pure Hilbert Einstein-like generally covariant theory. We introduce a change of variables that combines the conformal scale of the metric tensor with the brane fluctuations, so that the conformal scale becomes the modulus and the fluctuations become the angular field degrees of freedom of a polarly decomposed Higgs. When we assume that the four dimensional space-time background of the generally covariant theory is locally conformally flat and that the internal space is a squashed three-sphere, we arrive at one massless and three massive vector fields akin those in the Weinberg-Salam model and recover all the familiar ingredients of the symmetry broken bosonic Weinberg-Salam model, except that there ...
We inquire how the Weinberg-Salam Model can become embedded in a higher dimensional theory. For t... more We inquire how the Weinberg-Salam Model can become embedded in a higher dimensional theory. For this we consider a three-brane that moves under the influence of seven dimensional pure Einstein gravity. When we choose the four dimensional space-time to be locally conformally flat and the internal space to be a squashed three-sphere, and project onto the massless Kaluza-Klein modes, we arrive at one massless and three massive vector fields akin those in the Electroweak Theory. Using a change of variables we then identify the conformal scale with the modulus of the standard Electroweak Higgs Boson while the brane fluctuations become the angular field degrees of freedom of the Higgs. The ensuing low energy theory coincides with the standard bosonic Weinberg-Salam Model in the Coleman-Weinberg limit of the Higgs potential, except that now the couplings are not independent but are all determined by the squashing parameter while a Higgs mass emerges from the $A^2$-condensation of the inter...
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Papers by Sergey Slizovskiy