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M. Shifman

Publications and source records attributed to M. Shifman.

At least 73 records · Page 4Linked to original sources
arXiv2011

QCD Sum Rules: Bridging the Gap between Short and Large Distances

I discuss aspects of the QCD sum rule method which attracted theorists' attention in earnest at a relatively late stage and are not yet fully solved. At first I briefly review such general topics as the structure of the operator product expansion in QCD and intrinsic limitations of the quark-hadron duality concept. In the second part I comment on holographic constructions - a focus of the current efforts to say something new on QCD at strong coupling. Of particular interest to me is the recent derivation of the vacuum magnetic susceptibility due to Son and Yamamoto. Remarkably, their result is the same as that obtained previously by Vainshtein in the field-theoretic framework. For some reasons, the Vainshtein formula, unexpectedly, is not successfull numerically. This is a slightly modified version of the talk delivered at 15th International QCD Conference "QCD 10," June 28 - July 3, 2010, Montpellier, France.

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arXiv2011

Confined Magnetic Monopoles in Dense QCD

Non-Abelian strings exist in the color-flavor locked phase of dense QCD. We show that kinks appearing in the world-sheet theory on these strings, in the form of the kink-antikink bound pairs, are the magnetic monopoles --- descendants of the 't Hooft-Polyakov monopoles surviving in such a special form in dense QCD. Our consideration is heavily based on analogies and inspiration coming from certain supersymmetric non-Abelian theories. This is the first ever analytic demonstration that objects unambiguously identifiable as the magnetic monopoles are "native" to non-Abelian Yang-Mills theories (albeit our analysis extends only to the phase of the monopole confinement and has nothing to say about their condensation). Technically our demonstration becomes possible due to the fact that low-energy dynamics of the non-Abelian strings in dense QCD is that of the orientational zero modes. It is described by an effective two-dimensional CP(2) model on the string world sheet. The kinks in this model representing confined magnetic monopoles are in a highly quantum regime.

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arXiv2010

Perturbative Aspects of Heterotically Deformed CP(N-1) Sigma Model. I

In this paper we begin the study of renormalizations in the heterotically deformed N=(0,2) CP(N-1) sigma models. In addition to the coupling constant g^2 of the undeformed N=(2,2) model, there is the second coupling constant γdescribing the strength of the heterotic deformation. We calculate both βfunctions, β_g and β_γat one loop, determining the flow of g^2 and γ. Under a certain choice of the initial conditions, the theory is asymptotically free. The βfunction for the ratio ρ=γ^2/g^2 exhibits an infrared fixed point at ρ={1}{2}. Formally this fixed point lies outside the validity of the one-loop approximation. We argue, however, that the fixed point at ρ={1}{2} may survive to all orders. The reason is the enhancement of symmetry - emergence of a chiral fermion flavor symmetry in the heterotically deformed Lagrangian - at ρ={1}{2}. Next we argue that β_ρformally obtained at one loop, is exact to all orders in the large-N (planar) approximation. Thus, the fixed point at ρ= {1}{2} is definitely the feature of the model in the large-N limit.

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arXiv2010

Moduli Space Potentials for Heterotic non-Abelian Flux Tubes: Weak Deformation

We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and N_f flavors of massive quarks deformed by the mass term μfor the adjoint matter, W=μA^2, assuming that N\leq N_f<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized by W. They are referred to as F-term stabilized strings. We focus on the studies of such strings in the vacuum in which N squarks condense, at small μ, so that the Z_N strings preserve, in a sense, their BPS nature. We calculate string tensions both in the classical and quantum regimes. Then we translate our results for the tensions in terms of the effective low-energy weighted CP(N_f-1) model on the string world sheet. The bulk μ-deformation makes this theory N= (0,2) supersymmetric heterotic weighted CP(N_f-1) model in two dimensions. We find the deformation potential on the world sheet. This significantly expands the class of the heterotically deformed CP models emerging on the string world sheet compared to that suggested by Edalati and Tong. Among other things, we show that nonperturbative quantum effects in the bulk theory are exactly reproduced by the quantum effects in the world-sheet theory.

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arXiv2010

N=(0,2) Deformation of the N=(2,2) Wess-Zumino Model in Two Dimensions

We construct a simple N=(0,2) deformation of the two-dimensional Wess-Zumino model. In addition to superpotential, it includes a "twisted" superpotential. Supersymmetry may or may not be spontaneously broken at the classical level. In the latter case an extra right-handed fermion field ζ_R involved in the N=(0,2) deformation plays the role of Goldstino.

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arXiv2010

Large-N Solution of the Heterotic N=(0,2) Two-Dimensional CP(N-1) Model

We continue explorations of non-Abelian strings, focusing on the solution of a heterotic deformation of the CP(N-1) model with an extra right-handed fermion field and N=(0,2) supersymmetry. This model emerges as a low-energy theory on the worldsheet of the BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by a superpotential of a special type breaking N=2 supersymmetry down to N=1. Using large-N expansion we solve this model to the leading order in 1/N. Our solution exhibits spontaneous supersymmetry breaking for all values of the deformation parameter. We identify the Goldstino field. The discrete Z_{2N} symmetry is shown to be spontaneously broken down to Z_2; therefore, the worldsheet model has N strictly degenerate vacua (with nonvanishing vacuum energy). Thus, the heterotic CP(N-1) model is in the deconfinement phase. We can compare this dynamical pattern, on the one hand, with the N=(2,2) CP(N-1) model which has N degenerate vacua with unbroken supersymmetry, and, on the other hand, with nonsupersymmetric CP(N-1) model with split quasivacua and the Coulomb/confining phase. We determine the mass spectrum of the heterotic CP(N-1) model in the large-N limit.

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arXiv2010

Non-Abelian Strings and Axions

Axion-like fields can have a strong impact on non-Abelian strings. I discuss axion connection to such strings and its implications in two cases: (i) axion localized on the strings, and (ii) axions propagating in the four-dimensional bulk. Talk at the Workshop "Axions 2010", in honor of the 60-th birthday of Pierre Sikivie, University of Florida, January 15-17, 2010.

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arXiv2010

Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on Confining Strings

Recently we observed a crossover transition (in the Fayet-Iliopoulos parameter) from weak to strong coupling in N=2 supersymmetric QCD with the U(N) gauge group and N_f > N quark flavors. At strong coupling this theory can be described by a dual non-Abelian weakly coupled SQCD with the dual gauge group U(N_f-N) and N_f light dyon flavors. Both theories support non-Abelian strings. We continue the study of confinement dynamics in these theories, in particular, metamorphoses of excitation spectra, from a different side. A number of results obtained previously are explained, enhanced and supplemented by analyzing the world-sheet dynamics on the non-Abelian confining strings. The world-sheet theory is the two-dimensional N=(2,2) supersymmetric weighted CP(N_f-1) model. We explore the vacuum structure and kinks on the world sheet, corresponding to confined monopoles in the bulk theory. We show that (in the equal quark mass limit) these kinks fall into the fundamental representation of the unbroken global SU(N)\times SU(N_f-N)\timesU(1) group. This result confirms the presence of "extra" stringy meson states in the adjoint representation of the global group in the bulk theory. The non-Abelian bulk duality is in one-to-one correspondence with a duality taking place in the N=(2,2) supersymmetric weighted CP(N_f-1) model.

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arXiv2010

Higher Winding Strings and Confined Monopoles in N=2 SQCD

We consider composite string solutions in N=2 SQCD with the gauge group U(N), the Fayet--Iliopoulos term ξ\neq 0 and N (s)quark flavors. These bulk theories support non-Abelian strings and confined monopoles identified with kinks in the two-dimensional world-sheet theory. Similar and more complicated kinks (corresponding to composite confined monopoles) must exist in the world-sheet theories on composite strings. In a bid to detect them we analyze the Hanany--Tong (HT) model, focusing on a particular example of N=2. Unequal quark mass terms in the bulk theory result in the twisted masses in the N=(2,2) HT model. For spatially coinciding 2-strings, we find three distinct minima of potential energy, corresponding to three different 2-strings. Then we find BPS-saturated kinks interpolating between each pair of vacua. Two kinks can be called elementary. They emanate one unit of the magnetic flux and have the same mass as the conventional 't Hooft--Polyakov monopole on the Coulomb branch of the bulk theory (ξ=0). The third kink represents a composite bimonopole, with twice the minimal magnetic flux. Its mass is twice the mass of the elementary confined monopole. We find instantons in the HT model, and discuss quantum effects in composite strings at strong coupling. In addition, we study the renormalization group flow in this model.

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arXiv2009

LARGE EXTRA DIMENSIONS: Becoming acquainted with an alternative paradigm

This is a colloquium style pedagogical introduction to the paradigm of large extra dimensions. To be published in the Proceedings of the Workshop "Crossing the boundaries: Gauge dynamics at strong coupling," (May 14 - 17, 2009, Minneapolis), Eds. M. Peloso and A. Vainshtein, (World Scientific, Singapore, 2009), p. 3.

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arXiv2009

Non-Abelian Strings: From Weak to Strong Coupling and Back via Duality

The crossover transition from weak coupling at large ξto strong coupling at small ξis studied in N=2 supersymmetric gauge theory with the U(N) gauge group and N_f>N (here ξis the Fayet--Iliopoulos parameter). We find that at strong coupling a dual non-Abelian weakly coupled N=2 theory exists which describes low-energy physics at small ξ. The dual gauge group is U(N_f-N). The dual theory has N_f flavors of light dyons, to be compared with N_f quarks in the original U(N) theory. Both theories support non-Abelian strings. In each of these two regimes there are two varieties of physical excitations: elementary fields and nonperturbative composite states bound by confining strings. These varieties interchange upon transition from one regime to the other. We conjecture that the composite stringy states can be related to Seiberg's M fields.

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arXiv2009

Description of the Heterotic String Solutions in the M Model

We continue the study of heterotic non-Abelian BPS-saturated flux tubes (strings). Previously, such solutions were obtained in U(N) gauge theories: N=2 supersymmetric QCD deformed by superpotential terms μA^2 breaking N=2 supersymmetry down to N=1. In these models one cannot consider the limit μ\to\infty which would eliminate adjoint fields: the bulk theory develops a Higgs branch; the emergence of massless particles in the bulk precludes one from taking the limit μ\to\infty. This drawback is absent in the M model (hep-th/0701040) where the matter sector includes additional "meson" fields M introduced in a special way. We generalize our previous results to the M model, derive the heterotic string (the string world-sheet theory is a heterotic N=(2,0) sigma model, with the CP(N-1) target space for bosonic fields and an extra right-handed fermion coupled to the fermion fields of the N=(2,2) CP(N-1) model), and then explicitly obtain all relevant zero modes. This allows us to relate parameters of the microscopic M model to those of the world-sheet theory. The limit μ\to\infty is perfectly smooth. Thus, the full-blown and fully analyzed heterotic string emerges, for the first time, in the N=1 theory with no adjoint fields. The fate of the confined monopoles is discussed.

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arXiv2009

Quantum Fusion of Domain Walls with Fluxes

We study how fluxes on the domain wall world volume modify quantum fusion of two distant parallel domain walls into a composite wall. The elementary wall fluxes can be separated into parallel and antiparallel components. The parallel component affects neither the binding energy nor the process of quantum merger. The antiparallel fluxes, instead, increase the binding energy and, against naive expectations, suppress quantum fusion. In the small flux limit we explicitly find the bounce solution and the fusion rate as a function of the flux. We argue that at large (antiparallel) fluxes there exists a critical value of the flux (versus the difference in the wall tensions), which switches off quantum fusion altogether. This phenomenon of flux-related wall stabilization is rather peculiar: it is unrelated to any conserved quantity. Our consideration of the flux-related all stabilization is based on substantiated arguments that fall short of complete proof.

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arXiv2009

Quantum Fusion of Strings (Flux Tubes) and Domain Walls

We consider formation of composite strings and domain walls as a result of fusion of two elementary objects (elementary strings in the first case and elementary walls in the second) located at a distance from each other. The tension of the composite object T_2 is assumed to be less than twice the tension of the elementary object T_1, so that bound states are possible. If in the initial state the distance d between the fusing strings or walls is much larger than their thickness and satisfies the conditions T_1 d^2 >> 1 (in the string case) and T_1 d^3 >> 1 (in the wall case), the problem can be fully solved quasiclassically. The fusion probability is determined by the first, "under the barrier" stage of the process. We find the bounce configuration and its extremal action S_B. In the wall problem e^{-S_B} gives the fusion probability per unit time per unit area. In the string case, due to a logarithmic infrared divergence, the problem is well formulated only for finite-length strings. The fusion probability per unit time can be found in the limit in which the string length is much larger than the distance between two merging strings.

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arXiv2009

Non-Abelian Duality and Confinement in N=2 Supersymmetric QCD

In N=2 supersymmetric QCD with the U(N) gauge group and N_f>N we study the crossover transition from the weak coupling regime at large ξto strong coupling at small ξwhere ξis the Fayet--Iliopoulos parameter. We find that at strong coupling a dual non-Abelian weakly coupled N=2 theory exists which describes low-energy physics at small ξ. The dual gauge group is U(N_f-N) and the dual theory has N_f flavors of light dyons, to be compared with N_f quarks in the original U(N) theory. Both, the original and dual theories are Higgsed and share the same global symmetry SU(N) x SU(N_f-N) x U(1), albeit the physical meaning of the SU(N) and SU(N_f-N) factors is different in the large- and small-ξregimes. Both regimes support non-Abelian semilocal strings. In each of these two regimes particles that are in the adjoint representations with respect to one of the factor groups exist in two varieties: elementary fields and composite states bound by strings. These varieties interchange upon transition from one regime to the other. We conjecture that the composite stringy states can be related to Seiberg's M fields. The bulk duality that we observed translates into a two-dimensional duality on the world sheet of the non-Abelian strings. At large ξthe internal dynamics of the semilocal non-Abelian strings is described by the sigma model of N orientational and (N_f-N) size moduli, while at small ξthe roles of orientational and size moduli interchange. The BPS spectra of two dual sigma models (describing confined monopoles/dyons of the bulk theory) coincide. It would be interesting to trace parallels between the non-Abelian duality we found and string theory constructions.

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arXiv2009

Heterotic Flux Tubes in N=2 SQCD with N=1 Preserving Deformations

We consider non-Abelian BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Previously it was believed that worldsheet supersymmetry is "accidentally" enhanced due to the facts that N =(1,1) SUSY is automatically elevated up to N=(2,2) on CP(N-1) and, at the same time, there are no N=(0,2) generalizations of the bosonic CP(N-1) model. Edalati and Tong noted that the target space is in fact CP(N-1) x C rather than CP(N-1). This allowed them to suggest a "heterotic" N=(0,2) sigma model, with the CP(N-1) target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the N=(2,2) CP(N-1) model. We derive the heterotic N=(0,2) worldsheet model directly from the bulk theory. The relation between the bulk and worldsheet deformation parameters we obtain does not coincide with that suggested by Edalati and Tong at large values of the deformation parameter. For polynomial deformation superpotentials in the bulk we find nonpolynomial response in the worldsheet model. We find a geometric representation for the heterotic model. Supersymmetry is proven to be spontaneously broken for small deformations (at the quantum level). This confirms Tong's conjecture. A proof valid for large deformations will be presented in the subsequent publication.

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arXiv2009

Crossover between Abelian and non-Abelian confinement in N=2 supersymmetric QCD

In this paper we investigate the nature of the transition from Abelian to non-Abelian confinement (i.e. crossover vs. phase transition). To this end we consider the basic N=2 model where non-Abelian flux tubes (strings) were first found: supersymmetric QCD with the U(N) gauge group and N_f=N flavors of fundamental matter (quarks). The Fayet-Iliopoulos term ξtriggers the squark condensation and leads to the formation of non-Abelian strings. There are two adjustable parameters in this model: ξand the quark mass difference Δm. We obtain the phase diagram on the (ξ, Δm) plane. At large ξand small Δm the world-sheet dynamics of the string orientational moduli is described by N=2 two-dimensional CP(N-1) model. We show that as we reduce ξthe theory exhibits a crossover to the Abelian (Seiberg-Witten) regime. Instead of N^2 degrees of freedom of non-Abelian theory now only N degrees of freedom survive in the low-energy spectrum. Dyons with certain quantum numbers condense leading to the formation of the Abelian Z_N strings whose fluxes are fixed inside the Cartan subalgebra of the gauge group. As we increase N this crossover becomes exceedingly sharper becoming a genuine phase transition at N =\infty.

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