We study the String dual to N=1 SQCD deformed by a quartic superpotential in the quark superfields. We present a unified view of the previous results in the literature and find new exact solutions and new asymptotic solutions. Then we study the Physics encoded in these backgrounds, giving among other things a resolution to an old puzzle related to the beta function and a sufficient criteria for screening. We also extend our results to the SO(Nc) case where we present a candidate for the Wilson loop in the spinorial representation. Various aspects of this line of research are critically analyzed.
We match a few non chiral operators in the electric and magnetic descriptions of SQCD, suggesting the first evidence of electric-magnetic duality outside the chiral ring. Algebraically, these non chiral operators are a module of the chiral ring. Physically, the suggested correspondence essentially transforms certain electric gauge invariant composites containing the electric field strength into magnetic matter composites.
A new solution in the string background dual to N=1 SQCD-like theories is presented. The gauge coupling in this solution has walking property. The Wilson loop calculations show that quark anti-quark potential makes phase transitions. Additionally the effect of flavours on other solutions in this background is investigated by considering some unflavoured solutions and perturbing them with small parameter $x=\frac{N_{f}}{N_{c}}$.
The Affleck-Dine-Seiberg instanton generated superpotential for SQCD with Nf=Nc-1 flavours is explicitly derived from a local model of engineered intersecting D6-branes with a single E2-instanton. This computation extends also to symplectic gauge groups with Nf=Nc flavours.
We use the M theory approach of Witten to investigate N=1 SU($N_c$) SQCD with $N_f$ flavors. We reproduce the field theoretical results and identify in M theory the gluino condensate and the eigenvalues of the meson matrix. This approach allows us to identify the constant piece of the effective field theory coupling from which the coefficient of the one-loop $β$-function can be identified. By studying the area of the M-theory five-brane we investigate the stability of type IIA brane configurations. We prove that in a supersymmetric setup there is no force between static D4-branes that end on N…
In this paper we make further refinements to the duality proposed between N=1 SQCD and certain string (supergravity plus branes) backgrounds, working in the regime of comparable large number of colors and flavors. Using the string theory solutions, we predict different field theory observables and phenomena like Seiberg duality, gauge coupling and its running, the behavior of Wilson and 't Hooft loops, anomalous dimensions of the quark superfields, quartic superpotential coupling and its running, continuous and discrete anomaly matching. We also give evidence for the smooth interpolation betwe…
We calculate the scalar potential of supersymmetric QCD (in the regime N_f < N_c) coupled to N=1 supergravity with moduli-dependent gauge kinetic function and masses. The gauge dynamics are described by the Taylor-Veneziano-Yankielowicz superpotential for composite effective fields. The potential can be expanded about the ``truncated'' point in the gaugino and matter condensate directions in order to find corrections to the globally supersymmetric minimum. The results are relevant to the phenomenology of supersymmetry-breaking in string-inspired supergravity models, and also to recent work on …
We revisit N_f=N_c SQCD and its non-supersymmetric minima conjectured by Intriligator, Seiberg and Shih (ISS). We argue that the existence of such minima depends on the signs of three non-calculable parameters and that no evidence can be inferred by deforming the theory. We demonstrate this by studying a deformation of the theory which involves additional gauge singlets. In this case, the conjectured minimum is destabilized. We comment on the consequences of such singlets in models of direct mediation and in particular in the Pentagon model.
In this note we describe how N=1 SQCD-like theories with a large number of flavors can be given a dual description in terms of a string background containing a large number of additional D5-branes. The dual geometries account for the backreaction of the additional branes: they depend on the ratio between the number of flavors and colors of the gauge theory. This note is based on hep-th/0602027. We present here also a new set of solutions, which are not included in the original paper.
We give a topological classification of stable and unconfined massive particles and strings (and some instantons) in worldvolume theories of M5-branes and their dimensional reductions, generalizing Witten's classification of strings in SYM. In particular 4d N=2 SQCD softly broken to N=1 contains torsion (Douglas-Shenker) Z_N-strings and nontorsion (Hanany-Tong) Z-strings. Some of the former are stable when the flavor symmetry is gauged, while those that are not stable confine quarks and in some vacua even dyons into baryons. The nontorsion strings are stable if and only if all colors are locke…
We construct supergravity plus branes solutions, which we argue to be related to 4d N=1 SQCD with a quartic superpotential. The geometries depend on the ratio Nf/Nc which can be kept of order one, present a good singularity at the origin and are weakly curved elsewhere. We support our field theory interpretation by studying a variety of features like R-symmetry breaking, instantons, Seiberg duality, Wilson loops and pair creation, running of couplings and domain walls. In a second part of this paper, we address a different problem: the analysis of the interesting physics of different members o…
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 th…
We study the thermodynamics and the jet quenching parameter of a black hole solution dual to a SQCD-like plasma which includes the backreaction of fundamental flavors. The free energy is calculated in several ways, including some recently proposed holographic renormalization prescriptions. The validity of the latter is confirmed by the consistency with the other methods. The resulting thermodynamic properties are similar to the Little String Theory ones: the temperature is fixed at the Hagedorn value and the free energy is vanishing. Finally, an accurate analysis of the relevant string configu…
In a recent paper [1] we showed that N=1 supersymmetric QCD in the presence of certain superpotential deformations has a rich landscape of supersymmetric and non-supersymmetric vacua. In this paper we embed this theory in string theory as a low energy theory of intersecting NS and D-branes. We find that in the region of parameter space of brane configurations that can be reliably studied using classical string theory, the vacuum structure is qualitatively similar to that in the field theory regime. Effects that in field theory come from one loop corrections arise in string theory as classical …
We study vortex-strings in four-dimensional N=2 supersymmetric SU(Nc)xU(1) gauge theories with Nf hypermultiplets in the fundamental representation of SU(Nc) and general U(1) charges. If Nf>Nc, the vacuum is not gapped and the low-energy theory contains both the vacuum massless excitations and the string zero-modes. The question we address in this work is whether the vacuum and the string moduli decouple at low energies, allowing a description of the low-energy dynamics in terms of a two-dimensional theory on the string worldsheet. We find a simple condition controlling the bulk-string couplin…
We consider the relation between the Ω-deformed N=2 SQCD with the single deformation parameter and integrable models of the BCS-like superconductivity. It is argued that the vortex string worldsheet theory is related to the Russian Doll(RD) model of the truncated BCS superconductivity. We argue that the Ω-deformed gauge theory manifests the interesting cyclic RG behavior with the period of the RG cycle proportional to ε^{-1}. The deformed gauge theory can develop several non-perturbative scales. We conjecture on the monopole bound state interpretation of the Efimov tower.
Type II string theory compactified on a Calabi-Yau manifold, with a singularity modeled by a hypersurface in an orbifold, is considered. In the limit of vanishing string coupling, one expects a non gravitational theory concentrated at the singularity. It is proposed that this theory is holographicly dual to a family of ``non-critical'' superstring vacua, generalizing a previous proposal for hypersurfaces in flat space. It is argued that a class of such singularities is relevant for the study of non-trivial IR fixed points that appear in the moduli space of four-dimensional N=2 SQCD: SU(N_c) ga…
It has been shown that non-Abelian solitonic vortex string supported in four-dimensional (4D) N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and $N_f = 4$ quark flavors becomes a critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau noncompact threefold, namely, the conifold. The spectrum of low lying closed string states in the associated type IIA string theory was found and interpreted as a spectrum of hadrons in 4D N = 2 SQCD. In particular, the lowest string state appears to …
We present the configurations of intersecting branes in type IIA string theory corresponding to the meta-stable supersymmetry breaking vacua(hep-th/0608063) in the four-dimensional N=1 supersymmetric Yang-Mills theory coupled massive flavors with adjoint matter where the superpotential has three deformed terms.
It has been shown that non-Abelian solitonic vortex strings supported in four-dimensional (4D) ${\mathcal N}=2\;$ supersymmetric QCD (SQCD) with the U($N=2$) gauge group and $N_f=4$ quark flavors behave as critical superstrings. In addition to four translational moduli non-Abelian strings under consideration carry six orientational and size moduli. Together they form a ten-dimensional 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 $\mathbb{R}^4$ and a Calabi-Yau non-compact threefold $Y_6$, namely, the…
This paper could have been entitled "D branes and strings from flesh and blood." We study field theoretic prototypes of D branes/strings. To this end we consider (2+1)-dimensional domain walls in (3+1)-dimensional N=2 SQCD with SU(2) gauge group and two quark flavors in the fundamental representation. This theory is perturbed by a small mass term of the adjoint matter which, in the leading order in the mass parameter, does not break N=2 supersymmetry, and reduces to a (generalized) Fayet-Iliopoulos term in the effective low-energy N=2 SQED. We find 1/2 BPS-saturated domain wall solution interp…
We continue the study of heterotic non-Abelian BPS-saturated flux tubes (strings). Previously, such solutions were obtained [1] in a particular U(2) gauge theory: N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Here we generalize the previous results to U(N) gauge theories. As was suggested by Edalati and Tong [2], the string world sheet theory is 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…
We consider non-Abelian 1/2 BPS flux tubes (strings) in a deformed N=2 supersymmetric gauge theory, with mass terms mu_{1,2} of the adjoint fields breaking N=2 down to N=1. The main feature of the non-Abelian strings is the occurrence of orientational moduli associated with the possibility of rotations of their color fluxes inside a global SU(N) group. The bulk four-dimensional theory has four supercharges; half-criticality of the non-Abelian strings would imply then N=1 supersymmetry on the world sheet, i.e. two supercharges. In fact, superalgebra of the reduced moduli space has four supercha…
We embed the supersymmetry breaking mechanism in N=1 SQCD of hep-th/0602239 in a smooth superstring theory using D-branes in the background R^4 \times SL(2)_{k=1}/U(1) which smoothly captures the throat region of an intersecting NS5-brane configuration. A controllable deformation of the supersymmetric branes gives rise to the mass deformation of the magnetic SQCD theory on the branes. The consequent instability on the open string worldsheet can be followed onto a stable non-supersymmetric configuration of D-branes which realize the metastable vacuum configuration in the field theory. The new b…
Critical Non-Abelian Vortex String and 2D N=2 Black Hole
William I. Fine Theoretical Physics Institute, University of Minnesota（明尼苏达大学威廉·I·基础物理研究所）；Dept. Math., HSE University（高等经济大学数学系）；Theory Department of LPI（列宁格勒物理研究所理论部）；National Research Center “Kurchatov Institute”, Petersburg Nuclear Physics Institute（库尔恰托夫国家研究中心圣彼得堡核物理研究所）；HSE University（高等经济大学）
We consider a model which in a certain limit reduces to the large N ${\cal N}=1$ supersymmetric SU(N) gauge theory without matter. The gaugino condensate in this model is controlled by the dynamics of an additional singlet superfield. Using this model we explicitly construct BPS domain walls arising due to the chiral symmetry breaking. In particular, in the large N limit we obtain the exact shapes of the domain walls corresponding to solitons, and also of the domain walls interpreted as D-branes on which the SQCD string can end, whose existence was previously argued by Witten in the context of…
We consider N=1 supersymmetric quantum chromodynamics (SQCD) with the gauge group U(N_c) and N_c+N quark flavors. N_c flavors are massless; the corresponding squark fields develop (small) vacuum expectation values (VEVs) on the Higgs branch. Extra N flavors are endowed with small (and equal) mass terms. We study this theory through its Seiberg's dual: U(N) gauge theory with N_c +N flavors of "dual quark" fields plus a gauge-singlet mesonic field M. The original theory is referred to as "quark theory" while the dual one is termed "monopole theory." The suggested mild deformation of Seiberg's pr…
Hadrons in $\mathcal{N}=2$ supersymmetric QCD from non-Abelian string on 2D black hole
William I. Fine Theoretical Physics Institute, University of Minnesota（明尼苏达大学威廉·I·费因理论物理研究所）；Skoltech（斯科尔科沃科学技术大学）；Dept. Math., HSE University（高等经济大学数学系）；NRC ‘‘Kurchatov Institute’’ - PNPI（库尔恰托夫国家研究中心——彼得堡核物理研究所）；HSE University（高等经济大学）
We investigate neutralino dark matter from a string/M-theory perspective. Using the Kallosh-Linde (KL) scenario to stabilize the string moduli requires supersymmetry breaking for uplifting to a de Sitter vacuum. We consider the free magnetic dual description of $\mathcal{N}=1$ SUSY QCD with massive flavours, the Intriligator-Seiberg-Shih model (ISS), as an F-term dynamical SUSY breaking sector. This framework allows for a gravitino mass in the TeV range. Moreover, due to the plethora of particles from the ISS sector, we investigate the consequences of coupling the MSSM with the KL-ISS setup to…
We propose an electric-magnetic duality and conjecture an exact conformal window for a class of non-supersymmetric U(N_c) gauge theories with fermions in the (anti)symmetric representation of the gauge group and N_f additional scalar and fermion flavors. The duality exchanges N_c with N_f -N_c \mp 4 leaving N_f invariant, and has common features with Seiberg duality in N=1 SQCD with SU or SO/Sp gauge group. At large N the duality holds due to planar equivalence with N=1 SQCD. At finite N we embed these gauge theories in a setup with D-branes and orientifolds in a non-supersymmetric, but tachyo…
We study probe flavor branes supersymmetrically embedded in the Klebanov-Strassler background. The embedding is controlled by a single complex parameter mu related to the quark mass. We study the spectrum of the vector mesons as a function of mu and compare it with the experimental data. Assuming that the rho(2150) meson is a 3S mode we find a remarkable agreement with the masses of the lightest excited rho-mesons. Also, for a certain range of parameters our model exhibits an unusual behavior. The mesons built of the lighter quarks become more heavy than the ones built of the heavier quarks. W…
Supersymmetric gauge theories have had a significant impact on our understanding of QCD and of field theory in general. The phases of N=1 supersymmetric QCD (SQCD) are discussed, and the possibility of similar phases in non-supersymmetric QCD is emphasized. It is described how duality in SQCD links many previously known duality transformations that were thought to be distinct, including Olive-Montonen duality of N=4 supersymmetric gauge theory and quark-hadron duality in (S)QCD. A connection between Olive-Montonen duality and the confining strings of Yang-Mills theory is explained, in which a …
We study the quantum dynamics of vortex strings in N=1 SQCD with U(N_c) gauge group and N_f=N_c quarks. The classical worldsheet of the string has N=(0,2) supersymmetry, but this is broken by quantum effects. We show how the pattern of supersymmetry breaking and restoration on the worldsheet captures the quantum dynamics of the underlying 4d theory. We also find qualitative matching of the meson spectrum in 4d and the spectrum on the worldsheet.
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…
We show that the $4d$ ${\cal N}=1$ $SU(3)$ $N_f=6$ SQCD is the model obtained when compactifying the rank one E-string theory on a three punctured sphere (a trinion) with a particular value of flux. The $SU(6)\times SU(6)\times U(1)$ global symmetry of the theory, when decomposed into the $SU(2)^3\times U(1)^3\times SU(6)$ subgroup, corresponds to the three $SU(2)$ symmetries associated to the three punctures and the $U(1)^3 \times SU(6)$ subgroup of the $E_8$ symmetry of the E-string theory. All the puncture symmetries are manifest in the UV and thus we can construct ordinary Lagrangians flow…
Recently we discovered and discussed non-Abelian duality in the quark vacua of N=2 super-Yang-Mills theory with the U(N) gauge group and N_f flavors (N_f>N). Both theories from the dual pair support non-Abelian strings which confine monopoles. Now we introduce an N=2-breaking deformation, a mass term μ{\mathcal A}^2 for the adjoint fields. Starting from a small deformation we eventually make it large which enforces complete decoupling of the adjoint fields. We show that the above non-Abelian duality fully survives in the limit of N=1 SQCD, albeit some technicalities change. For instance, non-A…
We derive an exact string-like soliton solution of D=10 heterotic string theory. The solution possesses $SU(2)\times SU(2)$ instanton structure in the eight-dimensional space transverse to the worldsheet of the soliton.
A direct derivation of the string field theory action in the Witten's background independent open string theory for the case when ghosts and matter are decoupled is given and consequences are discussed.
We consider the tachyon potentials in closed and open-closed string theories. In doing so, we apply technique which proved to be useful in studying the open string tachyon potentials to the problem of interest.
Trying to quantize the string in a de Sitter spacetime, Miao Li, Wei Song and Yushu Song presents a solution for the string equation of motion (JHEP04(2007)042) that is not correct. This reopens the problem by them addressed.
In this Reply, using E.R. Bezerra de Mello's comment, I correct calculations and results presented in Phys. Lett. B 614 (2005) 140-142 about fine structure constant in the spacetime of a cosmic string.
We present a simple proof that self-avoiding fermionic strings solve formally (in a quantum mechanical sense) the QCD(U(Nc)) Loop Wave Equation written in terms of random loops
The high-energy behavior of string scattering in warped spacetimes is studied to all orders in perturbation theory. If one assumes that the theory is finite, the amplitudes exactly fall as powers of momentum.
We make a simple observation that the massless continuous spin representations of the Poincaré group are not present in perturbative string theory constructions. This represents one of the very few model-independent low-energy consequences of these models.
We consider N =1 supersymmetric QCD with the gauge group U(N) and N_f=N quark flavors. To get rid of flat directions we add a meson superfield. The theory has no adjoint fields and, therefore, no 't Hooft-Polyakov monopoles in the quasiclassical limit. We observe a non-Abelian Meissner effect: condensation of color charges (squarks) gives rise to confined monopoles. The very fact of their existence in N =1 supersymmetric QCD without adjoint scalars was not known previously. Our analysis is analytic and is based on the fact that the N =1 theory under consideration can be obtained starting from …
We discuss the singularities in the moduli space of string compactifications to six dimensions with $N=1$ supersymmetry. Such singularities arise from either massless particles or non-critical tensionless strings. The points with tensionless strings are sometimes phase transition points between different phases of the theory. These results appear to connect all known $N=1$ supersymmetric six-dimensional vacua.
In this Reply, using G.de.A.Marques' comment, we correct calculations and results presented in [Phys.Lett.B 632(2006) 151-154] about corrections to the fine structure constant in the spacetime of a cosmic string from the generalized uncertainty principle.
In recent work a multimonopole solution of heterotic string theory was obtained. The monopoles are noted to be stable, in contrast with analogous solutions of Einstein-Maxwell or Yang-Mills-dilaton theory. The existence of this and other classes of stable solitonic solutions in string theory thus provides a possible test for low-energy string theory as distinct from other gauge + gravity theories.
We study the Regge limit of string amplitudes within the model of Polchinski-Strassler for string scattering in warped spacetimes. We also present some numerical estimations of the Regge slopes. It is quite remarkable that the real values of the slopes are inside a range of ours.
We present a solution of M(atrix) theory describing type IIA fundamental string. Our construction is based on the central charge of the longitudinal membrane (= fundamental string), the BPS saturation condition and the relation between M(atrix) theory and supersymmetric Yang-Mills theory. The fundamental string corresponds to a photon in supersymmetric Yang-Mills theory.
We try to draw lessons for higher dimensions from the string representations recently derived for large $N$ Yang-Mills theory by Gross and Taylor, Kostov, and others, and call attention to three characteristics that should be expected of a string theory precisely equivalent to a higher dimensional gauge theory: continuous world-sheets; strong coupling at short distances; and negative weights. To appear in the proceedings of the Strings '93 Berkeley conference.
We show that the string tension in N=1 two-dimensional super Yang-Mills theory vanishes independently of the representation of the quark anti-quark external source. We argue that this result persists in SQCD_2 and in two-dimensional gauge theories with extended supersymmetry or in chiral invariant models with at least one massless dynamical fermion. We also compute the string tension for the massive Schwinger model, as a demonstration of the method of the calculation.
Following hep-th/0309238 relating the matrix string theory to the light-cone superstring field theory, we write down two supercharges in the matrix string theory explicitly. After checking the supersymmetry algebra at the leading order, we proceed to discuss higher-order contact terms.
Unified description of color-electric and color-magnetic strings in hybrid vacua of $\mathcal{N}=2$ supersymmetric QCD
William I. Fine Theoretical Physics Institute, University of Minnesota（明尼苏达大学威廉·I·基础理论物理研究所）；NRC “Kurchatov Institute” - PNPI（库尔恰托夫国家研究中心-库尔恰托夫物理研究所）；St. Petersburg State University（圣彼得堡国立大学）；Steklov Mathematical Institute（斯捷克洛夫数学研究所）；ITMO University（ITMO大学）；HSE University（高等经济学院）
Recently proposed by Hwang, Marnelius and Saltsidis zeta regularization of basic commutators in string theories is generalized to the string models with non-trivial vacuums. It is shown that implementation of this regularization implies the cancellation of dangerous terms in the commutators between Virasoro generators, which break Jacobi identity.
We consider a type IIA-like string theory with RR-flux in two dimension and propose its matrix model dual. This string theory describes a Majorana fermion in the two dimensional spacetime. We also discuss its scattering amplitudes both in the world-sheet theory and in the matrix model.
Using the spectral representation approach to the Zamolodchikov's c-function and the Maldacena conjecture for the D1-branes, we compute the entropy of type IIB strings. An agreement, up to a numerical constant which cannot be determined using this approach, with the Bekenstein-Hawking entropy is found.
