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M. Shifman

Publications and source records attributed to M. Shifman.

At least 19 recordsLinked to original sources
arXiv2024

QCD Chemistry: Remarks on Diquarks

In connection with recent discoveries of heavy-quark containing exotic states publications discussing $Qq$ diquarks ($Q,q$ stand for a heavy and light quarks, respectively) proliferated in the literature. After a brief summary of the diquark concept I review various general reasons why the $Qq$ diquark (with sufficinetly heavy $Q$) does not exist. Then I argue (this is the focus of my talk) that the most direct way to confirm non-existence of the $Qq$ diquarks is the study of pre-asymptotic corrections in the inclusive decays of $Qqq$ baryons, e.g. $\Lambda_b$. Since the $c$ quarks are much lighter than $b$, namely, $m_b^2/m_c^2\sim 11$, traces of the $cq$ attraction in the color anti-triplet spin-0 state may or may not be present in the $cqq$ baryons.

hep-ph↗
arXiv2024

Introduction to the second edition of "The Supersymmetric World"

The first Edition of this book was released in 2000, just before the symposium ``Thirty Years of Supersymmetry'' was held at the William I. Fine Theoretical Physics Institute (FTPI) of the University of Minnesota. Founders and trailblazers of supersymmetry descended on FTPI, as well as a large crowd of younger theorists deeply involved in research in this area. Since then 23 years have elapsed and significant changes happened in supersymmetry (SUSY). Its history definitely needs an update. Such an update is presented below. The Second Edition of the revised collection will be released in 2024.

physics.hist-ph↗
arXiv2022

OPE-based Methods in Nonperturbative QCD

I describe the inception and development of nonperturbative OPE-based methods in hadronic physics, such as the SVZ sum rules, inverse heavy quark mass expansion (IHQME) and so on and related topics.

hep-ph↗
arXiv2022

Historical curiosity: how asymptotic freedom of the Yang-Mills theory could have been discovered three times before Gross, Wilczek, and Politzer, but was not

This article was published in 2001 in Festschrift "At the Frontier of Particle Physics; Handbook of QCD", Ed. M. Shifman, (World Scientific, Singapore, 2001), Vol. 1, page 126. Asymptotic freedom as the basic property of QCD was discovered by Gross, Wilczek, and Politzer in 1973. Personal recollections of David Gross which are being published in this Volume vividly describe the historical background and the chain of events which led to this fundamental breakthrough. Unfortunately, I failed to obtain Politzer's side of the story. Some details can be found in an interview which Prof. Politzer gave to R. Crease and C. Mann on February 21, 1985 \cite{DP}. Below I acquaint the reader with the pre-1973 appearances of asymptotic freedom which, unfortunately, went unnoticed

physics.hist-ph↗
arXiv2020

Operator Product Expansion and Calculation of the Two-Loop Gell-Mann-Low Function

This work was carried out in 1985. It was published in Russian in Yad. Fiz. 44, 498 (1986) [English translation Sov. J. Nucl. Phys. 44, 321 (1986)]. None of these publications are available on-line. Submitting this paper to ArXiv will make it accessible. *** A simple method is developed that makes it possible to determine the $k$-loop coefficient of the $β$-function if the operator product expansion for certain polarization operators in the $(k -1)$ loop is known. The calculation of the two-loop coefficient of the Gell-Mann-Low function becomes trivial -- it reduces to a few algebraic operations on already known expressions. As examples, spinor, scalar, and supersymmetric electrodynamics are considered. Although the respective results for $β^{(2)}$ are known in the literature, both the method of calculation and certain points pertaining to the construction of the operator product expansion are new.

hep-th↗
arXiv2020

The Beginning of the Nuclear Age

The article below is based on lectures delivered to new students remotely in the course of orientation. It presents the quantum theory tree from its inception a century ago till today. The main focus is on the nuclear physics - HEP branch.

physics.hist-ph↗
arXiv2020

String "Baryon'' in Four-Dimensional $\mathcal{N} = 2$ Supersymmetric QCD from 2D-4D Correspondence

We study non-Abelian vortex strings in four-dimensional (4D) $\mathcal{N} = 2$ supersymmetric QCD with U$(N=2)$ gauge group and $N_f=4$ flavors of quark hypermultiplets. It has been recently shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D $\mathcal{N} = 2$ supersymmetric QCD. In particular, the lowest string state appears to be a massless BPS "baryon." Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the conformal world-sheet theory on the non-Abelian string -- the so called weighted $\mathcal{N} = (2,2)$ supersymmetric $\mathbb{CP}$ model. Its target space is given by the six-dimensional non-compact Calabi-Yau space $Y_6$, the conifold. We use mirror description of the model to study the BPS kink spectrum and its transformations on curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of the complex structure of the conifold is associated with the emergence of a non-perturbative Higgs branch in 4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum expectation value of the massless BPS "baryon" previously found in string theory.

hep-th↗
arXiv2019

Musings on the Current Status of HEP

I briefly summarize my personal opinions on the current status of HEP theory and comment on the so-called "non-empiric confirmation."

physics.hist-ph↗
arXiv2019

Quantizing a solitonic string

Quite often the zero mode dynamics on solitonic vortices are described by a non-conformal effective world-sheet sigma model (WSSM). We address the problem of solitonic string quantization in this case. As well-known, only crfitical strings with superconformal WSSMs are self-consistent in ultra-violet (UV) domain. Thus, we look for the appropriate UV completion of the low-energy non-conformal WSSM. We ague that for the solitonic strings supported in well-defined bulk theories the UV complete WSSM has a UV fixed point which can be used for string quantization. As an example, we consider BPS non-Abelian vortices supported by four-dimensional (4D) \ntwo SQCD with the gauge group U$(N)$ and $N_f$ quark multiplets where $N_f\ge N$. In addition to translational moduli the non-Abelian vortex under consideration carries orientational and size moduli. Their low-energy dynamics are described by a two-dimensional \ntwot supersymmetric weighted model, namely, $\mathbb{WCP}(N, N_f-N)$. Given our UV completion of this WSSM we find its UV fixed point. The latter defines a superconformal WSSM. We observe two cases in which this conformal WSSM, combined with the free theory for four translational moduli, has ten-dimensional target space required for superstrings to be critical.

hep-th↗
arXiv2018

Hadrons of N=2 Supersymmetric QCD in Four Dimensions from Little String Theory

It was recently shown that non-Abelian vortex strings supported in a version of four-dimensional N=2 supersymmetric QCD (SQCD) become critical superstrings. In addition to four translational moduli, non-Abelian strings under consideration have six orientational and size moduli. Together they form a ten-dimensional target space required for a superstring to be critical, namely, the product of the flat four-dimensional space and conifold -- a non-compact Calabi-Yau threefold. In this paper we report on further studies of low-lying closed string states which emerge in four dimensions and identify them as hadrons of our four-dimensional N=2 SQCD. We use the approach based on "little string theory," describing critical string on the conifold as a non-critical $c=1$ string with the Liouville field and a compact scalar at the self-dual radius. In addition to massless hypermultiplet found earlier we observe several massive vector multiplets and a massive spin-2 multiplet, all belonging to the long (non-BPS) representations of N=2 supersymmetry in four dimensions. All the above states are interpreted as baryons formed by a closed string with confined monopoles attached. Our construction presents an example of a "reverse holography."

hep-th↗
arXiv2018

Supersymmetric Tools in Yang-Mills Theories at Strong Coupling: the Beginning of a Long Journey

Development of holomorphy-based methods in super-Yang-Mills theories started in the early 1980s and lead to a number of breakthrough results. I review some results in which I participated. The discovery of Seiberg's duality and the Seiberg-Witten solution of ${\cal N}=2$ Yang-Mills were the milestones in the long journey of which, I assume, much will be said in other talks. I will focus on the discovery (2003) of non-Abelian vortex strings with various degree of supersymmetry, supported in some four-dimensional Yang-Mills theories and some intriguing implications of this discovery. One of the recent results is the observation of a soliton string in the bulk ${\cal N}=2$ theory with the $U(2)$ gauge group and four flavors, which can become critical in a certain limit. This is the case of a "reverse holography," with a very transparent physical meaning.

hep-th↗
arXiv2017

Index Theorem for non-Supersymmetric Fermions Coupled to a non-Abelian String and Electric Charge Quantization

Non-Abelian strings are considered in {\em non}-supersymmetric theories with fermions in various appropriate representations of the gauge group U($N$). We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases, we observe a non-trivial $N$ dependence.

hep-th↗
arXiv2017

Fradkin-Shenker Continuity and "Instead-of-Confinement" Phase

In 1979 Fradkin and Shenker observed \cite{Frad} that if one considers a Yang-Mills theory fully Higgsed by virtue of scalar fields in the fundamental representation of the ${\rm SU}(N)$ gauge group there is no phase transition in passing from the Higgs regime (weak coupling) to the "QCD confinement" regime at strong coupling. The above two regimes are continuously connected. We combine this observations with lessons from supersymmetric gauge theories which show that the Higgs phase is continuously connected to what is called "instead-of-confinement" phase rather than the phase with quark confinement. In the "instead-of-confinement" phase monopoles are confined and play a role of "constituent" quarks inside hadrons. In contrast, the Seiberg-Witten phase of quark confinement is not analytically connected to the Higgs phase. We propose dedicated lattice studies of Yang-Mills theories with scalar quarks.

hep-ph↗
arXiv2017

Critical Non-Abelian Vortex in Four Dimensions and Little String Theory

As was shown recently, non-Abelian vortex strings supported in four-dimensional ${\cal N}=2$ supersymmetric QCD with the U(2) gauge group and $N_f=4$ quark multiplets (flavors) become critical superstrings. In addition to the translational moduli non-Abelian strings under consideration carry six orientational and size moduli. Together they form a ten-dimensional target space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space and a Calabi-Yau non-compact threefold, namely, the conifold. We study closed string states which emerge in four dimensions (4D) and identify them with hadrons of four-dimensional ${\cal N}=2$ QCD. One massless state was found previously: it emerges as a massless hypermultiplet associated with the deformation of the complex structure of the conifold. In this paper we find a number of massive states. To this end we exploit the approach used in LST, "Little String Theory," namely equivalence between the critical string on the conifold and non-critical $c=1$ string with the Liouville field and a compact scalar at the self-dual radius. The states we find carry "baryonic" charge (its definition differs from standard). We interpret them as "monopole necklaces" formed (at strong coupling) by the closed string with confined monopoles attached.

hep-th↗
arXiv2017

N=(0,2) Deformation of CP(1) Model: Two-dimensional Analog of N=1 Yang-Mills Theory in Four Dimensions

We consider two-dimensional $\mathcal{N}=(0,2)$ sigma models with the CP(1) target space. A minimal model of this type has one left-handed fermion. Nonminimal extensions contain, in addition, $N_f$ right-handed fermions. Our task is to derive expressions for the $β$ functions valid to all orders. To this end we use a variety of methods: (i) perturbative analysis; (ii) instanton calculus; (iii) analysis of the supercurrent supermultiplet (the so-called hypercurrent) and its anomalies, and some other arguments. All these arguments, combined, indicate a direct parallel between the heterotic $\mathcal{N}=(0,2)$ CP(1) models and four-dimensional super-Yang-Mills theories. In particular, the minimal $\mathcal{N}=(0,2)$ CP(1) model is similar to ${\mathcal N}=1$ supersymmetric gluodynamics. Its exact $β$ function can be found; it has the structure of the Novikov-Shifman-Vainshtein-Zakharov (NSVZ) $β$ function of supersymmetric gluodynamics. The passage to nonminimal $\mathcal{N}=(0,2)$ sigma models is equivalent to adding matter. In this case an NSVZ-type exact relation between the $β$ function and the anomalous dimensions $γ$ of the "matter" fields is established. We derive an analog of the Konishi anomaly. At large $N_f$ our $β$ function develops an infrared fixed point at small values of the coupling constant (analogous to the Banks-Zaks fixed point). Thus, we reliably predict the existence of a conformal window. At $N_f=1$ the model under consideration reduces to the well-known $\mathcal{N}=(2,2)$ CP(1) model.

hep-th↗
arXiv2016

Non-Abelian Vortex in Four Dimensions as a Critical Superstring

We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional N=2 supersymmetric QCD with the U(2) gauge group, N_f=4 quark flavors and the Fayet-Iliopoulos term. Under certain conditions the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a two-dimensional sigma model with the target space {R}^4\times Y_6 where Y_6 is a non-compact Calabi-Yau conifold. The closed string states which emerge in four dimensions (4D) are identified with hadrons of 4D bulk N=2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole-monopole baryon of the 4D theory (at strong coupling).

hep-th↗
arXiv2016

Introduction to "Standing together in Troubled Times"

This Introduction opens the book {\sl Standing Together in Troubled Times} which presents a story of friendship between Wolfgang Pauli, one of the greatest theoretical physicists of the 20th century, and Charlotte Houtermans. They met at the very onset of the quantum era, in the late 1920s in Germany where Charlotte was a physics student at Göttingen University. At that time Göttingen was right at the heart of groundbreaking developments in physics. Both Pauli and Houtermans personally knew major participants in the quantum revolution. Caught between two evils -- German National Socialism and Soviet Communism -- Charlotte Houtermans would have likely perished if it were not for the brotherhood of physicists: Niels Bohr, Wolfgang Pauli, Albert Einstein, James Franck, Max Born, Robert Oppenheimer and many other noted scientists who tried to save friends and colleagues (either leftist sympathizers or Jews) who were in mortal danger of becoming entrapped in a simmering pre-WWII Europe. This book is based on newly discovered documents from the Houtermans family archive, including Pauli's numerous letters to Houtermans, her correspondence with other great physicists, her diaries, and interviews with her children. Almost all documents presented in this book are being published for the first time.

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