2,507 research outputs found

### Glueball and meson spectrum in large-N massless QCD

We provide outstanding numerical evidence that in large-N massless QCD the
joint spectrum of the masses squared, for fixed integer spin s and unspecified
parity and charge conjugation, obeys exactly the following laws: m_k^2 =
(k+s/2) Lambda_QCD^2 for s even, m_k^2 = 2(k+s/2) Lambda_QCD^2 for s odd, k =
1,2,... for glueballs, and m_n^2 = 1/2 (n+s/2) Lambda_QCD^2, n = 0,1,... for
mesons. One of the striking features of these laws is that they imply that the
glueball and meson masses squared form exactly-linear Regge trajectories in the
large-N limit of massless QCD, all the way down to the low-lying states: A fact
unsuspected so far. The numerical evidence is based on lattice computations by
Meyer-Teper in SU(8) YM for glueballs, and by Bali et al. in SU(17) quenched
massless QCD for mesons, that we analyze systematically. The aforementioned
spectrum for spin-0 glueballs is implied by a Topological Field Theory
underlying the large-N limit of YM, whose glueball propagators satisfy as well
fundamental universal constraints arising from the asymptotic freedom and the
renormalization group. No other presently existing model meets both the
infrared spectrum and the ultraviolet constraints. We argue that some features
of the aforementioned spectrum of glueballs and mesons of any spin could be
explained by the existence of a Topological String Theory dual to the
Topological Field Theory.Comment: 9 pages, 2 figures; added some comments on the different accuracy in
the glueball and meson sectors; references update

### Renormalization in large-$N$ QCD is incompatible with open/closed string duality

Solving by a canonical string theory, of closed strings for the glueballs and
open strings for the mesons, the 't Hooft large-$N$ expansion of QCD is a
long-standing problem that resisted all the attempts despite the advent of the
celebrated gauge/gravity duality in the framework of string theory. We
demonstrate that in the canonical string framework such a solution does not
actually exist because an inconsistency arises between the renormalization
properties of the QCD S matrix at large $N$ -- a consequence of the asymptotic
freedom (AF) -- and the open/closed duality of the would-be string solution.
Specifically, the would-be open-string one-loop corrections to the tree
glueball amplitudes must be ultraviolet (UV) divergent. Hence, naively, the
inconsistency arises because these amplitudes are dual to tree closed-string
diagrams, which are universally believed to be both UV finite -- since they are
closed-string tree diagrams -- and infrared finite because of the glueball mass
gap. In fact, the inconsistency follows from a low-energy theorem of the NSVZ
type that controls the renormalization in QCD-like theories. The inconsistency
extends to the would-be canonical string for a vast class of 't Hooft large-$N$
QCD-like theories including $\mathcal{N}=1$ SUSY QCD. We also demonstrate that
the presently existing SUSY string models with a mass gap -- such as
Klebanov-Strassler, Polchinski-Strassler (PS) and certain PS variants -- cannot
contradict the above-mentioned results since they are not asymptotically free.
Moreover, we shed light on the way the open/closed string duality may be
perturbatively realized in these string models compatibly with a mass gap in
the 't Hooft-planar closed-string sector and the low-energy theorem because of
the lack of AF. Finally, we suggest a noncanonical way-out for QCD-like
theories based on topological strings on noncommutative twistor space.Comment: 23 pages, 1 figure; this is the version published in Phys. Lett. B:
it contains an extended exposition of the main results, and a discussion on
the way the open/closed string duality may be realized in presently existing
string models with a mass gap that are not asymptotically fre

### Some comments on S-duality in four-dimensional QCD

We show that a necessary condition, for the partition function of
four-dimensional Yang-Mills theory to satisfy a S-duality property, is that
certain functional determinants, generated by the dual change of variables,
cancel each other. This result holds up to non-topological boundary terms in
the dual action and modulo the problem of field-strength copies for the Bianchi
identity constraint.Comment: 4 pages, latex, no figures. Basic references on duality adde

### An asymptotic solution of large-$N$ $QCD$, and of large-$N$ $\mathcal{N}=1$ $SUSY$ $YM$

We find an asymptotic solution for two- and three-point correlators of local
gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$,
in terms of glueball and meson propagators, by means of a new purely
field-theoretical technique that we call the asymptotically-free bootstrap. The
asymptotically-free bootstrap exploits the lowest-order conformal invariance of
connected correlators of gauge invariant composite operators in perturbation
theory, the renormalization-group improvement, and a recently-proved asymptotic
structure theorem for glueball and meson propagators, that involves the unknown
particle spectrum and the anomalous dimension of operators for fixed spin. In
principle the asymptotically-free bootstrap extends to all the higher-spin two-
and three-point correlators whose lowest-order conformal limit is non-vanishing
in perturbation theory, and by means of the operator product expansion to the
corresponding asymptotic multi-point correlators as well. Besides, the
asymptotically-free bootstrap provides asymptotic $S$-matrix amplitudes in
massless large-$N$ $QCD$ in terms of glueball and meson propagators as opposed
to perturbation theory. Remarkably, the asymptotic $S$-matrix depends only on
the unknown particle spectrum, but not on the anomalous dimensions. Moreover,
the asymptotically-free bootstrap applies to large-$N$ $\mathcal{N}=1$ $SUSY$
$YM$ as well. Practically, as just a few examples among many more, it follows
the structure of the light by light scattering amplitude, of the pion form
factor, and the associated vector dominance. Theoretically, the asymptotic
solution sets the strongest constraints on any actual solution of large-$N$
$QCD$ (and of large-$N$ $\mathcal{N}=1$ $SUSY$ $YM$), and in particular on any
string solution.Comment: 56 pages, latex; more details and remarks, and some simplification;
references added; typos fixed; talk at the conference: HP2: High Precision
for Hard Processes, September 3-5, (2014), associated to the workshop:
Prospects and Precision at the Large Hadron Collider at 14 TeV, at the
Galileo Galilei Institute for Theoretical Physics, Florence, Ital

### The Abelian projection versus the Hitchin fibration of K(D) pairs in four-dimensional QCD

We point out that the concept of Abelian projection gives us a physical
interpretation of the role that the Hitchin fibration of parabolic K(D) pairs
plays in the large-N limit of four-dimensional QCD. This physical
interpretation furnishes also a simple criterium for the confinement of
electric fluxes in the large-N limit of QCD. There is also an alternative,
compatible interpretation, based on the QCD string.Comment: 11 pages, latex, no figures, a misprint correcte

### Large-N limit and contact terms in unbroken YM_4

I characterize the structure of the master field for $F^{0}_{z \bar z}$ in
$SU(\infty)$-$YM_4$ on a product of two Riemann surfaces $Z \times W$ in the
gauge $F^{ch}_{z \bar z}=0$ as the sum of a `bulk' constant term and of
delta-like `contact' terms.\\ The contact terms may occur because the
localization of the functional integral at $N=\infty$ on a master orbit of a
constant connection under the action of singular gauge transformations is still
compatible with the large-$N$ factorization and translational invariance.\\ In
addition I argue that if the gauge group is unbroken and there is a mass gap,
that is if the theory confines, the functional measure at $N=\infty$, in the
gauge $F^{ch}_{z \bar z}=0$, must be localized on the moduli space of flat
connections with punctures on $Z \times W$.Comment: 8 pages, latex, no figure

### Asymptotic Freedom versus Open/Closed Duality in Large-N QCD

The solution of the large-N 't Hooft limit of QCD is universally believed to
be a String Theory of Closed Strings in the Glueball Sector and of Open Strings
in the Meson Sector. Yet, we prove a no-go theorem, that the large-N limit of
QCD with massless quarks, or more generally, that the large-N limit of a vast
class of confining, i.e. with a Mass Gap in the Glueball Sector,
asymptotically-free Gauge Theories coupled to matter fields with no mass scale
in perturbation theory cannot be a canonically-defined String Theory of Closed
and Open Strings, i.e. admitting Open/Closed Duality. The no-go theorem occurs
because Open/Closed Duality, implying that the ultraviolet divergences of
annulus diagrams in the Open Sector arise from infrared divergences of tadpoles
of massless particles in the Closed Sector, turns out to be incompatible with
the existence of the Mass Gap in the Glueball Sector of confining
asymptotically-free theories with no mass scale in perturbation theory in
which, as for example in QCD, the first coefficient of the beta function for 't
Hooft gauge coupling gets $1/N$ corrections due to the matter fields. Moreover,
we suggest a way-out to the no-go theorem on the basis of a new non-canonical
construction of the String S-matrix for asymptotically-free Gauge Theories such
as large-N QCD, involving Topological Strings on Non-Commutative Twistor Space.Comment: 8 pages; the main argument is extended to a punctured sphere with a
boundary loop; further references and acknowledgement

### Exact beta function and glueball spectrum in large-N Yang Mills theory

In the pure large-N Yang-Mills theory there is a quasi-BPS sector that is
exactly solvable at large N. It follows an exact beta function and the glueball
spectrum in this sector. The main technical tool is a new holomorphic loop
equation for quasi-BPS Wilson loops, that occurs as a non-supersymmetric
analogue of Dijkgraaf-Vafa holomorphic loop equation for the glueball
superpotential of n=1 SUSY gauge theories. The new holomorphic loop equation is
localized, i.e. reduced to a critical equation, by a deformation of the loop
that is a vanishing boundary in homology, somehow in analogy with Witten's
cohomological localization by a coboundary deformation in SUSY gauge theories.Comment: PDF, 11 pages, talk at EPS-HEP 2009; added a footnote on the
fluctuations of surface operators as published in Po

### Large-N Wilsonian beta function in SU(N) Yang-Mills theory by localization on the fixed points of a semigroup contracting the functional measure

In a certain (non-commutative) version of large-N SU(N) Yang-Mills theory
there are special Wilson loops, called twistor Wilson loops for geometrical
reasons, whose v.e.v. is independent on the parameter that occurs in their
operator definition. There is a semigroup that acts on the parameter by
rescaling and on the functional measure, resolved into anti-selfdual orbits by
a non-supersymmetric version of the Nicolai map, by contracting the support of
the measure. As a consequence the twistor Wilson loops are localized on the
fixed points of the semigroup of contractions. This localization is a
non-supersymmetric analogue of the localization that occurs in the Nekrasov
partition function of the n=2 SUSY YM theory on the fixed points of a certain
torus action on the moduli space of (non-commutative) instantons. One main
consequence of the localization in the large-N YM case, as in the n=2 SUSY YM
case, is that the beta function of the Wilsonian coupling constant in the
anti-selfdual variables is one-loop exact. Consequently the large-N Yang-Mills
canonical beta function has a NSVZ form that reproduces the first two universal
perturbative coefficients.Comment: 7 pages, latex; extended version of the talk at Lattice 2010; some
arguments have been sharpened; the paper is now considerably shorter
according to the requirements of the Lattice 2010 committe

### Chemical descriptors, convexity and structure of density matrices in molecular systems

The electron energy and density matrices in molecular systems are convex in
respect of the number of particles. So that, the chemical descriptors based on
their derivatives present the hamper of discontinuities for isolated systems
and consequently higher order derivatives are undefined. The introduction of
the interaction between the physical domain with an environment induces a
coherent structure for the density matrix in the grand-canonical formulation
suppressing the discontinuities leading to the proper definitions of the
descriptors.Comment: 6 pages, 0 figure

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