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Mikhail Shifman

Publications and source records attributed to Mikhail Shifman.

70 records · Page 4Linked to original sources
arXiv2013

Heterotic N=(0,2) CP(N-1) Model with Twisted Masses

We present a two-dimensional heterotic N=(0,2) CP(N-1) model with twisted masses. It is supposed to describe internal dynamics of non-Abelian strings in massive N=2 SQCD with N=1-preserving deformations. We present gauge and geometric formulations of the world-sheet theory and check its N=(0,2) supersymmetry. It turns out that the set of twisted masses in the heterotic model has N complex mass parameters, rather than N-1. In the general case, when all mass parameters are nonvanishing, N=(0,2) supersymmetry is spontaneously broken already at the classical level. If at least one of the above mass parameters vanishes, then N=(0,2) is unbroken at the classical level. The spontaneous breaking of supersymmetry in this case occurs through nonperturbative effects.

hep-th↗
arXiv2013

Low energy dynamics of gapless and quasi-gapless modes of vortices in superfluid $^3$He-B

We discuss the low energy effective dynamics of gapless excitations of the mass vortices of systems similar to the Ginzburg-Landau description of superfluid helium-3 in the bulk B phase. Our approach is to determine the vortex solution by considering a specific ansatz for the order parameter and minimizing the free energy. The conditions on the $β_i$ coefficients required for the stability of the various solutions for the order parameter are calculated. By considering the symmetries that are broken by the vortex solutions we are able to generate the moduli fields associated with the low energy excitations of the vortices. Using these fields we determine the effective free energy describing the dynamics of these excitations.

cond-mat.other↗
arXiv2013

Twisted-Mass Potential on the Non-Abelian String World Sheet Induced by Bulk Masses

We derive the twisted-mass potential in N=(2,2) CP(N-1) theory on the world sheet of the non-Abelian string from the bulk N=2 theory with massive (s)quarks by determining the profile functions of the adjoint fields. Although this potential was indirectly found some time ago, this is the first direct derivation from the bulk. As an application of the adjoint field profiles, we compute and confirm the $ | μσ| $ potential (where $ σ$ is a scalar field in the gauge supermultiplet) which arises in the effective two-dimensional theory on the string due to the supersymmetry breaking bulk mass term $ μA^2 $ for the adjoint matter.

hep-th↗
arXiv2013

Non-Abelian Quasi-Gapless Modes Localized on Mass Vortices in Superfluid 3He-B

Kelvin waves or Kelvons have been known for a long time as gapless excitations propagating along superfluid vortices. These modes can be interpreted as the Nambu-Goldstone excitations arising from the spontaneous breaking of the translational symmetry. Recently a different type of gapless excitation localized on strings -- the so-called non-Abelian mode -- attracted much attention in high-energy physics. We discuss their relevance in condensed matter physics. Although we failed to find exactly gapless non-Abelian modes, non-Abelian rotational quasigapless excitations are argued to exist on the mass vortices in the B phase of the superfluid 3He, due to the fact that the order parameter in 3He-B is tensorial. While the U(1) rotational excitations are well established in vortices with asymmetric cores, the non-Abelian rotational excitations belonging to the same family were not considered. In the general case they are coupled with the translational modes.

cond-mat.other↗
arXiv2012

2D-4D Correspondence: Towers of Kinks versus Towers of Monopoles in N=2 Theories

We continue to study the BPS spectrum of the N=(2,2) CP(N-1) model with the Z_N-symmetric twisted mass terms. We focus on analysis of the "extra" towers found previously in [1], and compare them to the states that can be identified in the quasiclassical domain. Exact analysis of the strong-coupling states shows that not all of them survive when passing to the weak-coupling domain. Some of the states decay on the curves of the marginal stability (CMS). Thus, not all strong-coupling states can be analytically continued to weak coupling to match the observable bound states. At weak coupling, we confirm the existence of bound states of topologically-charged kinks and elementary quanta. Quantization of the U(1) kink modulus leads to formation of towers of such states. For the Z_N-symmetric twisted masses their number is by far less than N-1 as was conjectured previously. We investigate the quasiclassical limit and show that out of N possible towers only two survive in the spectrum for odd N, and a single tower for even N. In the case of CP^2 theory the related CMS are discussed in detail. In these points we overlap and completely agree with the results of Dorey and Petunin. We also comment on 2D-4D correspondence.

hep-th↗
arXiv2011

Quantum Dynamics of Low-Energy Theory on Semilocal Non-Abelian Strings

Recently a low-energy effective theory on non-Abelian semilocal vortices in SQCD with the U(N) gauge group and N + \tilde{N} quark flavors was obtained in field theory arXiv:1104.2077. The result is exact in a certain limit of large infrared cut-off. The resulting model was called the zn model. We study quantum dynamics of the zn model in some detail. First we solve it at large N in the leading order. Then we compare our results with those of Hanany and Tong hep-th/0403158 (the HT model) who based their derivation on a certain type-IIA formalism, rather than on a field-theory construction. In the 't Hooft limit of infinite N both model's predictions are identical. At finite N our calculations agree with the Hanany-Tong results only in the BPS sector. Beyond the BPS sector there is no agreement between the zn and HT models. Finally, we study perturbation theory of the zn model from various standpoints.

hep-th↗
arXiv2011

BPS Spectrum of Supersymmetric CP(N-1) Theory with Z_N Twisted Masses

We revisit the BPS spectrum of the supersymmetric CP(N-1) two-dimensional model with Z_N-symmetric twisted masses m_l (l=0,1, ..., N-1). A related issue we address is that of the curves of marginal stability (CMS) in this theory. Previous analyses were incomplete. We close the gap by exploiting a number of consistency conditions. In particular, we amend the Dorey formula for the BPS spectrum. Our analysis is based on the exact Veneziano--Yankielowicz-type superpotential and on the strong-coupling spectrum of the theory found from the mirror representation at small masses, |m_l| << Λ. We show that at weak coupling the spectrum, with necessity, must include N-1 BPS towers of states, instead of just one, as was thought before. Only one of the towers is seen in the quasiclassical limit. We find the corresponding CMS for these towers, and argue that in the large-N limit they become circles, filling out a band on the plane of a single mass parameter of the model at hand. Inside the CMS, N-1 towers collapse into N stable states.

hep-th↗
arXiv2008

QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations

We consider QCD-like theories with one massless fermion in various representations of the gauge group SU$(N)$. The theories are formulated on $R_3\times S_1$. In the decompactification limit of large $r(S_1)$ all these theories are characterized by confinement, mass gap and spontaneous breaking of a (discrete) chiral symmetry ($χ$SB). At small $r(S_1)$, in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double trace deformation. With these deformation, the theories at hand are at weak coupling at small $r(S_1)$ and yet exhibit basic features of the large-$r(S_1)$ limit: confinement and $χ$SB. We calculate the string tension, mass gap, bifermion condensates and $θ$ dependence. The double-trace deformation becomes dynamically irrelevant at large $r(S_1)$. Despite the fact that at small $r(S_1)$ confinement is Abelian, while it is expected to be non-Abelian at large $r(S_1)$, we argue that small and large-$r(S_1)$ physics are continuously connected. If so, one can use small-$r(S_1)$ laboratory to extract lessons about QCD and QCD-like theories on $R_4$.

hep-th↗
arXiv2007

Planar Limit of Orientifold Field Theories and Emergent Center Symmetry

We consider orientifold field theories (i.e. SU(N) Yang--Mills theories with fermions in the two-index symmetric or antisymmetric representations) on R3xS1 where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang--Mills. The latter has Z_N center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z_N symmetric to Z_N broken phase applies. At the Lagrangian level the orientifold theories have at most a Z_2 center. We discuss how the full Z_N center symmetry dynamically emerges in the orientifold theories in the limit N-->infinity. In the confining phase the manifestation of this enhancement is the existence of stable k-strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang--Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.

hep-th↗
arXiv2007

A note on C-Parity Conservation and the Validity of Orientifold Planar Equivalence

We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermions in vector-like - but otherwise generic - representations of the gauge group. QCD, supersymmetric Yang-Mills theory, and orientifold field theories, all belong to this class. We argue that charge conjugation is not spontaneously broken as long as Lorentz invariance is maintained. Uniqueness of the vacuum state in pure Yang-Mills theory (without fermions) and convergence of the expansion in fermion loops are key ingredients. The fact that C-invariance is conserved has an interesting application to our proof of planar equivalence between supersymmetric Yang-Mills theory and orientifold field theory on R4, since it allows the use of charge conjugation to connect the large-N limit of Wilson loops in different representations.

hep-th↗
arXiv2000

Marginal Stability and the Metamorphosis of BPS States

We discuss the restructuring of the BPS spectrum which occurs on certain submanifolds of the moduli/parameter space -- the curves of the marginal stability (CMS) -- using quasiclassical methods. We argue that in general a `composite' BPS soliton swells in coordinate space as one approaches the CMS and that, as a bound state of two `primary' solitons, its dynamics in this region is determined by non-relativistic supersymmetric quantum mechanics. Near the CMS the bound state has a wave function which is highly spread out. Precisely on the CMS the bound state level reaches the continuum, the composite state delocalizes in coordinate space, and restructuring of the spectrum can occur. We present a detailed analysis of this behavior in a two-dimensional N=2 Wess-Zumino model with two chiral fields, and then discuss how it arises in the context of `composite' dyons near weak coupling CMS curves in N=2 supersymmetric gauge theories. We also consider cases where some states become massless on the CMS.

hep-th↗
arXiv1999

Instantons Versus Supersymmetry: Fifteen Years Later

An introduction to the instanton formalism in supersymmetric gauge theories is given. We explain how the instanton calculations, in conjunction with analyticity in chiral parameters and other general properties following from supersymmetry, allow one to establish exact results in the weak and strong coupling regimes. Some key applications are reviewed, the main emphasis is put on the mechanisms of the dynamical breaking of supersymmetry.

hep-th↗
arXiv1998

More on Supersymmetric Domain Walls, N Counting and Glued Potentials

Various features of domain walls in supersymmetric gluodynamics are discussed. We give a simple field-theoretic interpretation of the phenomenon of strings ending on the walls recently conjectured by Witten. An explanation of this phenomenon in the framework of gauge field theory is outlined. The phenomenon is argued to be particularly natural in supersymmetric theories which support degenerate vacuum states with distinct physical properties. The issue of existence (or non-existence) of the BPS saturated walls in the theories with glued (super)potentials is addressed. The amended Veneziano-Yankielowicz effective Lagrangian belongs to this class. The physical origin of the cusp structure of the effective Lagrangian is revealed, and the limitation it imposes on the calculability of the wall tension is explained. Related problems are considered. In particular, it is shown that the so called discrete anomaly matching, when properly implemented, does not rule out the chirally symmetric phase of supersymmetric gluodynamics, contrary to recent claims.

hep-th↗
arXiv1995

Two Phases of Supersymmetric Gluodynamics

We argue that supersymmetric gluodynamics has two phases with equivalent infrared behavior, one of which is asymptotically free and another one is superstrongly coupled in the ultraviolet domain.

hep-th↗
arXiv1995

Matching Conditions and Duality in N=1 SUSY Gauge Theories in the Conformal Window

We discuss duality in $N=1$ SUSY gauge theories in Seiberg's conformal window, $(3N_c/2)<N_f<3N_c$. The 't Hooft consistency conditions -- the basic tool for establishing the infrared duality -- are considered taking into account higher order $α$ corrections. The conserved (anomaly free) $R$ current is built to all orders in $α$. Although this current contains all orders in $α$ the 't Hooft consistency conditions for this current are shown to be one-loop. This observation thus justifies Seiberg's matching procedure. We also briefly discuss the inequivalence of the ``electric" and ``magnetic" theories at short distances.

hep-th↗