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M. Shifman

Publications and source records attributed to M. Shifman.

At least 37 records · Page 2Linked to original sources
arXiv2016

Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions

Recently a special vortex string was found [5] in a class of soliton vortices supported in four-dimensional Yang-Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang-Mills theory has the U(2) gauge group and the Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP(2,2) model. The full target space is R_4\times Y_6 where Y_6 is a non-compact Calabi-Yau space. We study the above vortex string from the standpoint of string theory, focusing on the massless states in four dimensions. In the generic case all massless modes are non-normalizable, hence, no massless gravitons or vector fields are predicted in the physical spectrum. However, at the selfdual point (at strong coupling) weighted CP(2,2) admits deformation of the complex structure, resulting in a single massless hypermultiplet in the bulk. We interpret it as a composite "baryon."

hep-th↗
arXiv2016

Heterotic Non-Abelian String of a Finite Length

We consider non-Abelian strings in N=2 supersymmetric QCD with the U$(N)$ gauge group and $N_f=N$ quark flavors deformed by a mass term for the adjoint matter. This deformation breaks N=2 supersymmetry down to N=1. Dynamics of orientational zero modes on the string world sheet are described then by CP$(N-1)$ model with N=(0,2) supersymmetry. We study the string of a finite length $L$ assuming compactification on a cylinder (periodic boundary conditions). The world-sheet theory is solved in the large-$N$ approximation. We find a rich phase structure in the $(L, \,u)$ plane where $u$ is a deformation parameter. At large $L$ and intermediate $u$ we find a phase with broken $Z_{2N}$ symmetry, $N$ vacua and a mass gap. At large values of $L$ and $u$ still larger we have the $Z_{2N}$-symmetric phase with a single vacuum and massless fermions. In both phases N=(0,2) supersymmetry is spontaneously broken. We also observe a phase with broken SU$(N)\;$ symmetry at small $L$. In the latter phase the mass gap vanishes and the vacuum energy is zero in the leading $1/N$ approximation. However, we expect that $1/N$ corrections will break N=(0,2) supersymmetry. We also discuss how this rich phase structure matches the N=(2,2) limit in which the world-sheet theory has a single phase with the mass gap independent of $L$.

hep-th↗
arXiv2016

Dynamically Emergent Flavor in a Confining Theory with Unbroken Chiral Symmetry

I discuss "truncated" QCD studied recently by Glozman et al. through numerical simulations. For two flavors it was observed that truncation restores the full chiral U(2)\times U(2) symmetry of the Lagrangian. Moreover, additional enhancement of the above symmetry connecting representations with distinct Lorentz spins was observed. I argue that the chiral symmetry restoration in a confining theory could entail emergent (extra) dynamical flavors which would show up in the spectrum of color-singlet particles provided their mass \neq 0. As an example, I consider truncated QCD with a single massless Dirac quark. Assuming the validity of the above observations,I demonstrate how a dynamical SU(2)_{fl} symmetry could emerge for massive spin-1 mesons without contradicting general principles.

hep-ph↗
arXiv2015

Critical String from Non-Abelian Vortex in Four Dimensions

In a class of non-Abelian solitonic vortex strings supported in certain N=2 super-Yang-Mills theories we search for the vortex which can behave as a critical fundamental string. We use the Polchinski-Strominger criterion of the ultraviolet completeness. We identify an appropriate four-dimensional bulk theory: it has the U(2) gauge group, the Fayet-Iliopoulos term and four flavor hypermultiplets. It supports semilocal vortices with the world-sheet theory for orientational (size) moduli described by the weighted CP(2,2) model. The latter is superconformal. Its target space is six-dimensional. The overall Virasoro central charge is critical. We show that the world-sheet theory on the vortex supported in this bulk model is the bona fide critical string.

hep-th↗
arXiv2015

Introduction to Collection "Physics in a Mad World" (an Abridged Version)

This Introduction opens the collection "Physics in A Mad World" devoted to two outstanding physicists whose destinies were deeply intertwined with the tragedies and drama of the times in which they lived. Friedrich (Fritz) Houtermans was the first to understand why stars shine. He endured Stalin's prisons in the Moscow of the late 1930s, then faced the Gestapo in Germany. In the early 1970s, Yuri Golfand was among the discoverers of theoretical supersymmetry, a concept which completely changed mathematical physics in the 21st century. After his discovery, his research institution in Moscow fired him. He knew the humiliations of the Brezhnev regime firsthand, blacklisted and unemployed for the rest of the decade due to his desire to emigrate to Israel. This introduction gives a detailed review of background and supplemental information to the events described in the three main essays authored by V. Frenkel, B. Eskin and B. Bolotovsky who presented captivating stories of the physicists' lives, as told by their friends, colleagues and relatives.

physics.hist-ph↗
arXiv2015

Derivation of the exact expression for the D function in N=1 SQCD

We discuss various details of our derivation of the exact expression for the Adler D function in N=1 supersymmetric QCD (SQCD). This exact formula relates the D function to anomalous dimensions of the matter superfields. Our perturbative derivation refers to the D function defined in terms of the bare coupling constant in the case of using the higher covariant derivative regularization. The exact expression for this function is obtained by direct summation of supergraphs to all orders in the non-Abelian coupling constant. As we argued previously, our formula should be valid beyond perturbation theory too. The perturbative result we present here coincides with the general formula order by order. We discuss consequences for N=1 SQCD in the conformal window. It is noted that our exact relation can allow one to determine the (infrared) critical anomalous dimension of the Seiberg M field present in the dual theory.

hep-th↗
arXiv2015

IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories

We use the "conspiracy" between infrared (IR) renormalons and condensates in the operator product expansion for correlation functions to make predictions concerning the structure of singularities in the Borel plane for the perturbative series in quantum field theories with different levels of supersymmetry. The same conspiracy can be used for establishing the absence of condensates or IR renormalons in gauge theories with an IR conformal regime or fully Higgsed gauge theories. The absence of the renormalon-induced factorial divergence implies that instanton contributions (where present) must be well-defined. We show that the conventional bubble-chain method for detecting renormalon-induced factorial divergences in these theories is not sufficient.

hep-th↗
arXiv2014

Exact Adler Function in Supersymmetric QCD

The Adler function D is found {\em exactly} in supersymmetric QCD. Our exact formula relates D(Q^2) to the anomalous dimension of the matter superfields γ(α_s(Q^2)). En rout we prove another theorem: the absence of the so-called singlet contribution to D. While such singlet contributions are present in individual supergraphs, they cancel in the sum.

hep-th↗
arXiv2014

Resurgence, Operator Product Expansion, and Remarks on Renormalons in Supersymmetric Yang-Mills

I discuss similarities and differences between the resurgence program in quantum mechanics and the operator product expansion in strongly coupled Yang-Mills theories. In ${\mathcal N}=1$ super-Yang-Mills renormalons possess peculiar features that make them different from renormalons in QCD. Their conventional QCD interpretation does not seem to be applicable in supersymmetric Yang-Mills in a straightforward manner.

hep-th↗
arXiv2014

Lessons from supersymmetry: "Instead-of-Confinement" Mechanism

We review physical scenarios in different vacua of N=2 supersymmetric QCD deformed by the mass term μfor the adjoint matter. This deformation breaks supersymmetry down to N=1 and, at large μ, the theory flows to N=1 SQCD. We focus on dynamical scenarios which can serve as prototypes of what we observe in real-world QCD. The so-called r=N vacuum is especially promising in this perspective. In this vacuum an "instead-of-confinement" phase was identified previously, which is qualitatively close to the conventional QCD confinement: the quarks and gauge bosons screened at weak coupling, at strong coupling evolve into monopole-antimonopole pairs confined by non-Abelian strings. We review genesis of this picture.

hep-th↗
arXiv2014

Two-Dimensional Sigma Models Related to Non-Abelian Strings in Super-Yang-Mills

We review diverse two-dimensional models emerging on the world sheet of non-Abelian strings in the low-energy limit. Non-Abelian strings are supported in a class of four-dimensional bulk theories with or without supersymmetry. In supersymmetric bulk theories we are mostly interested in BPS-saturated strings. Some of these two-dimensional models, in particular, heterotic models, were scarcely studied in the past, if at all. Our main emphasis is on the heterotic N=(0,2) models. We describe their large-N solution. We briefly comment on N=(0,1) models although so far they are not obtained on the the world sheet of non-Abelian strings.

hep-th↗
arXiv2014

N=1 Duality in the Chiral Limit from N=2 Duality

We study a deformation of N=2 supersymmetric QCD with U(N) gauge group and N_f quark flavors induced by the mass term μfor the adjoint matter which breaks supersymmetry down to N=1 QCD. Recently this deformation was shown to lead to a weakly coupled dual theory only in two particular sets of vacua: the r=N vacuum and the so-called zero vacua which can be found at r< N_f-N, where r is the number of condensed quarks. For small quark masses and intermediate values of μthe gauge group of the dual theory is U(N_f-N)\times U(1)^{2N-N_f} where the Abelian sector is heavy and can be integrated out. However, at larger values of μthe Abelian sector enters the strong coupling regime. We show that the 't Hooft matching conditions in the chiral limit require the Seiberg neutral meson field M from this sector to become light. In the r=N vacuum M is constructed of a monopole and antimonopole connected by a confining magnetic strings while in the zero vacua it is built of a quark and antiquark connected by a confining electric strings.

hep-th↗
arXiv2014

More on the Abrikosov Strings with Non-Abelian Moduli

We continue explorations of deformed Abrikosov-Nielsen-Olesen (ANO) strings, with non-Abelian moduli on the world sheet. In a simple model with an extra field we find classically stable ANO and non-Abelian strings. The tension of the latter is a few percent lower than the tension of the ANO string. Then we calculate the interpolating field configuration. Once the kink mass $M_k$ and the difference of tensions $ΔT$ are found we calculate the decay rate of the ANO string with a higher tension ("false vacuum") into the non-Abelian string with the lower tension ("genuine vacuum") through the "bubble" formation in the quasiclassical approximation.

hep-th↗
arXiv2014

Large-N Solution of the Heterotic CP(N-1) Model with Twisted Masses

We address a number of unanswered questions in the N=(0,2)-deformed CP(N-1) model with twisted masses. In particular, we complete the program of solving CP(N-1) model with twisted masses in the large-N limit. In hep-th/0512153 nonsupersymmetric version of the model with the Z_N symmetric twisted masses was analyzed in the framework of Witten's method. In arXiv:0803.0698 this analysis was extended: the large-N solution of the heterotic N=(0,2) CP(N-1) model with no twisted masses was found. Here we solve this model with the twisted masses switched on. Dynamical scenarios at large and small m are studied (m is the twisted mass scale). We found three distinct phases and two phase transitions on the m plane. Two phases with the spontaneously broken Z_N-symmetry are separated by a phase with unbroken Z_N. This latter phase is characterized by a unique vacuum and confinement of all U(1) charged fields ("quarks"). In the broken phases (one of them is at strong coupling) there are N degenerate vacua and no confinement, similarly to the situation in the N=(2,2) model. Supersymmetry is spontaneously broken everywhere except a circle |m|=Λin the Z_N-unbroken phase. Related issues are considered. In particular, we discuss the mirror representation for the heterotic model in a certain limiting case.

hep-th↗
arXiv2014

Quantum Deformation of the Effective Theory on Non-Abelian string and 2D-4D correspondence

We explore non-Abelian strings in the r=N-1 vacuum of N=2 supersymmetric QCD with the gauge group U(N) and N_f flavors of quarks (N_f\geq N), where r is the number of condensed quarks. N=2 supersymmetry is broken down to N=1 by a small mass term for the adjoint matter. We discover that the low-energy two-dimensional theory on the string world-sheet receives nonperturbative corrections from the bulk, through the bulk gaugino condensate. This is in contradistinction with the r=N vacuum situation, in which nonperturbative effects on the world sheet are determined by internal dynamics of the world-sheet theory. The 2D-4D correspondence (the coincidence of spectra of two-dimensional kinks and four-dimensional monopoles) remains valid in the BPS sector. Nonperturbative bulk effects deforming the weighted CP model on the world sheet are found by virtue of the method of resolvents suggested by Gaiotto, Gukov and Seiberg for surface defects. In the r=N vacuum the gaugino condensate in the bulk vanishes, and there are no "outside" nonperturbative corrections on the world sheet.

hep-th↗
arXiv2013

New and Old about Renormalons: in Memoriam Kolya Uraltsev

I summarize what we know of renormalons from the 1970s and 80s: their uses and theoretical status. It is emphasized that renormalons in QCD are closely related to the Wilsonean operator product expansion (OPE) - a setup ideally suited for dealing with the factorially divergent series reflecting infrared dynamics. I discuss a breakthrough proposal due to Uraltsev et al. to use renormalons to evaluate nonperturbative (power) corrections in the processes without OPE. Some fresh ideas which were put forward recently are briefly discussed too, with emphasis on a possible relationship between resurgence via trans-series and OPE. This article is devoted to the memory of my friend Kolya Uraltsev. I should emphasize that these are my personal recollections. Other people who closely knew Kolya may or may not agree with my opinions.

hep-th↗
arXiv2013

Degeneracy between Abelian and Non-Abelian Strings

In a model that supports both Abelian (Abrikosov-Nielsen-Olesen) and non-Abelian strings we analyze the parameter space to find examples in which these strings not only coexist but are degenerate in tension. We prove that both solutions are locally stable, i.e there are no negative modes in the string background. The tension degeneracy is achieved at the classical level and is expected to be lifted by quantum corrections. The set up of the model, analogous to that of Witten's superconducting cosmic strings, had been extended to include non-Abelian strings.

hep-th↗