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.
We review the recently constructed `double field theory' which introduces in addition to the conventional coordinates associated to momentum modes coordinates associated to winding modes. Thereby, T-duality becomes a global symmetry of the theory, which can be viewed as an `O(D,D) covariantization' of the low-energy effective space-time action of closed string theory. We discuss its symmetries with a special emphasis on the relation between global duality symmetries and local gauge symmetries.
Suppose a regularised functional integral depends holomorphically on a parameter that receives only a finite renormalization. Can one expect the correlation functions to retain the analyticity in the parameter after removal of the cutoff(s)? We examine the issue in the Sinh-Gordon theory by computing the intrinsic 4-point coupling as a function of the Lagrangian coupling β. Drawing on the conjectured triviality of the model in its functional integral formulation for β^2 > 8π, and the weak-strong coupling duality in the bootstrap formulation on the other hand, we conclude that the operations: `…
We construct the Komar integral for axion-dilaton gravity using Wald's formalism and momentum maps and we use it to derive a Smarr relation for stationary axion-dilaton black holes. While the Wald-Noether 2-form charge is not invariant under SL(2,R) electric-magnetic duality transformations because Wald's formalism does not account for magnetic charges and potentials, the Komar integral constructed with it turns out to be invariant and, in more general theories, it will be fully symplectic invariant. We check the Smarr formula obtained with the most general family of static axion-dilaton black…
It is widely believed that the emergent magnetic gauge symmetry of SQCD is analogous to a hidden local symmetry (HLS). We explore this idea in detail, deriving the entire (spontaneously broken) magnetic theory by applying the HLS formalism to spontaneously broken SU(N) SQCD. We deduce the Kähler potential in the HLS description, and show that gauge and flavour symmetry are smoothly restored along certain scaling directions in moduli space. We propose that it is these symmetry restoring directions, associated with the R-symmetry of the theory, that allow full Seiberg duality. Reconsidering the …
T-duality in M(atrix) theory has been argued to be realized as Morita equivalence in Yang-Mills theory on a non-commutative torus (NCSYM). Even though the two have the same structure group, they differ in their action since Morita equivalence makes crucial use of an additional modulus on the NCSYM side, the constant Abelian magnetic background. In this paper, we reanalyze and clarify the correspondence between M(atrix) theory and NCSYM, and provide two resolutions of this puzzle. In the first of them, the standard map is kept and the extra modulus is ignored, but the anomalous transformation i…
We investigate the transformation of entanglement entropy under dualities, using the Kramers-Wannier duality present in the transverse field Ising model as our example. Entanglement entropy between local spin degrees of freedom is not generically preserved by the duality; instead, entangled states may be mapped to states with no local entanglement. To understand the fate of this entanglement, we consider two quantitative descriptions of degrees of freedom and their transformation under duality. The first involves Kraus operators implementing the partial trace as a quantum channel, while the se…
It is known that, in the static gauge, the world-volume and the transverse Kaluza-Klein (KK) reductions of the O-plane effective actions on a circle satisfy the T-duality constraint for arbitrary base space background. In this paper we show that due to the presence of the second fundamental form in the D-brane couplings at order $α'$ and higher, the T-duality is satisfied only for a subclass of couplings for arbitrary base space background. They are $m=0$ couplings where $m$ is the number of $\tilde{B}$-field (without derivative on it). For $m>0$ couplings, the base space metric must be block-…
I put forward the low-energy confining asymptote of the solution $<W_{C}>$ (valid for large macroscopic contours C of the size $>>1/Λ_{QCD}$) to the large N Loop equation in the D=4 U(N) Yang-Mills theory with the asymptotic freedom in the ultraviolet domain. Adapting the multiscale decomposition characteristic of the Wilsonean renormgroup, the proposed Ansatz for the loop-average is composed in order to sew, along the lines of the bootstrap approach, the large N weak-coupling series for high-momentum modes with the $N\to{\infty}$ limit of the recently suggested stringy representation of the 1…
We show how to complement Feynman's exponential of the action so that it exhibits a Z_2 duality symmetry. The latter illustrates a relativity principle for the notion of quantum versus classical.
In addition to the double-dimensional reduction procedure that employs world-volume Killing symmetries of $p$-brane supergravity solutions and acts diagonally on a plot of $p$ versus spacetime dimension $D$, there exists a second procedure of ``vertical'' reduction. This reduces the transverse-space dimension via an integral that superposes solutions to the underlying Laplace equation. We show that vertical reduction is also closely related to the recently-introduced notion of intersecting $p$-branes. We illustrate this with examples, and also construct a new $D=11$ solution describing four in…
We reconstruct non-trivial 6d theories obtained by Blum and Intriligator by considering IIB or SO(32) 5 branes at ALE spaces in the language of Hanany Witten setups. Using ST duality we make the equivalence of the two approaches manifest, thereby uncovering several new T-duality relations between the group theoretic data describing the embedding of the instantonic 5 brane in the ALE and brane positions in the Hanany Witten language. We construct several new 6d theories, which can be understood as arising on 5 branes in IIB orientifolds with oppositely charged orientifold planes recently introd…
We present a dual formulation of the Cosserat theory of elasticity. In this theory a local element of an elastic body is described in terms of local displacement and local orientation. Upon the duality transformation these degrees of freedom map onto a coupled theory of a vector-valued one-form gauge field and an ordinary $U(1)$ gauge field. We discuss the degrees of freedom in the corresponding gauge theories, the defect matter and coupling to the curved space.
The Carroll group was originally introduced by Levy-Leblond [1] by considering the limit of the Poincaré group as $c\to0$. In this paper an alternative definition, based on the geometric properties of a non-Minkowskian, non-Galilean but nevertheless boost-invariant, space-time structure is proposed. A "duality" with the Galilean limit $c\to\infty$ is established. Our theory is illustrated by Carrollian electromagnetism.
U($N$) supersymmetric Yang-Mills theory naturally appears as the low-energy effective theory of a system of $N$ D-branes and open strings between them. Transverse spatial directions emerge from scalar fields, which are $N\times N$ matrices with color indices; roughly speaking, the eigenvalues are the locations of D-branes. In the past, it was argued that this simple 'emergent space' picture cannot be used in the context of gauge/gravity duality, because the ground-state wave function delocalizes at large $N$, leading to a conflict with the locality in the bulk geometry. In this paper we show t…
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On R^d the new theory differs from the original one by the spectrum of operators. Sometimes the local operators are the same but there are different line operators, surface operators, etc. The effects of the added topological degrees of freedom are more dramatic when we compactify R^d, and they are crucial in the context of electric-magnetic duality. We explore several examples including Dijkgraaf-Witten theories and their generalizations both in the continuum and …
We present a field theoretical description of quarkyonic matter consisting of quark, nucleon and ghost fields coupling to mesonic degrees of freedom. The ghosts are present to cancel over-counting of nucleon states that are Pauli blocked by the quark Fermi sea. Such a theory becomes an effective field theory of nucleons at low baryon density, and as such will reproduce nucleonic matter phenomenology. This theory can accommodate chiral symmetry restoration and the dynamical generation of a shell of nucleons at the Fermi surface. It is valid for finite temperature and density. In such a theory, …
A planar boundary introduced à la Symanzik in the 5D topological BF theory, with the only requirement of locality and power counting, allows to uniquely determine a gauge invariant, non topological 4D Lagrangian. The boundary condition on the bulk fields is interpreted as a duality relation for the boundary fields, in analogy with the fermionization duality which holds in the 3D case. This suggests that the 4D degrees of freedom might be fermionic, although starting from a bosonic bulk theory. The method we propose to dimensionally reduce a Quantum Field Theory and to identify the resulting de…
We describe the supersymmetrization of two formulations of free noncommutative planar particles -- in coordinate space with higher order Lagrangian [1] and in the framework of Faddeev and Jackiw [2,3], with first order action. In nonsupersymmetric case the first formulation after imposing subsidiary condition eliminating internal degrees of freedom provides the second formulation. In supersymmetric case one can also introduce the split into ``external'' and ``internal'' degrees of freedom both describing supersymmetric models.
Recently the multitude of vacua in string theory have led some authors to advocate the anthropic principle as a possible resolution for the contrived set of parameters that seem to govern our universe. I suggest that string theories should be viewed as effective theories, and hence of limited utility rather than as ``theories of everything''. I propose that quantum gravity should admit a form of determinism and that the self-dual points under phase-space duality should play a prominent role in the vacuum selection principle.
(abridged)The achievements of the present work include: a) A clarification of the multiple definition given by Bergmann of the concept of {\it (Bergmann) observable. This clarification leads to the proposal of a {\it main conjecture} asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). b) The analysis of the so-called {\it Hole} phenomenology in strict connection with the Hamiltonian treatment of the initial value …
The twist construction is a geometric T-duality that produces new manifolds from old, works well with for example hypercomplex structures and is easily inverted. It tends to destroy properties such as the hyperKähler condition. On the other hand modifications preserve the hyperKähler property, but do not have an obvious inversion. In this paper we show how elementary deformations provide a link between the two constructions, and use the twist construction to build hyperKähler and strong HKT structures. In the process, we provide a full classification of complete hyperKähler four-manifolds with…
We use gauge/gravity duality to study the thermodynamics of a field theory with asymptotic freedom in the ultraviolet and a fixed point in the infrared. We find a high temperature quark-gluon phase and a low T conformal unparticle phase. The phase transition between the phases is of first order or continuous, depending on the ratio of the radii of asymptotic AdS5 spaces at T=0 and T=infinity. This is a prediction from a model of gauge/gravity duality, not yet verified on the field theory side.
The 2-dimensional version of the Schwarz and Sen duality model (Tseytlin model) is analyzed at the classical and quantum levels. The solutions are obtained after removing the gauge dependent sector using the Dirac method. The Poincarè invariance is verified at both levels. An extension with global supersymmetry is also proposed.
We use gauge/gravity duality to study vector meson (J/Ψ, ρ_0, Ω, Φ) production in electron-proton scattering, in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by pomeron exchange. Our approach considers the pomeron at strong coupling, described by the graviton Regge trajectory in AdS space with a hard-wall to mimic confinement effects. Both the proton and vector mesons are described by simple holographic wave functions in AdS. This model agrees with HERA H1 data with a χ^2 per degree of freedom be…
In this article we study the noncommutative description of the DBI Lagrangian and its T-dual counterpart. We restrict the freedoms of the noncommutativity parameters of these Lagrangians. Therefore the noncommutativity parameter, the effective metric, the effective coupling constant of the string and the extra modulus ${\tilde Φ}$ of the effective T-dual theory, can be expressed in terms of the closed string variables $g$, $B$, $g_s$ and the noncommutativity parameter of the effective theory of open string.
We consider a simple model of large-Nc QCD defined by a spectrum consisting of an infinite set of equally spaced zero-width vector resonances. This model is an excellent theoretical laboratory for investigating certain approximation schemes which have been used recently in calculations of hadronic parameters, such as the Minimal Hadronic Approximation. We also comment on some of the questions concerning issues of local duality versus global duality and finite-energy sum rules.
In this article we probe the proposed holographic duality between $T\bar{T}$ deformed two dimensional conformal field theory and the gravity theory of $\rm AdS_3$ with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $T\bar{T}$ CFT in a Euclidean plane and in a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in $\rm AdS_3$ with the corresponding cutoff surface, given a hologra…
A topological fact about eleven dimensions is used to motivate a potential new duality in M-theory. We complete the discussion of consistent limits of M-theory raised in a previous paper to include gravitational anomaly cancelation and four-form flux quantization in the context of the $M^{10}\times S^1/Z_2$ compactifications. A suprise is found: If one includes a $Z_2$ anomaly which exists only in 8k+3 dimensions then there are two distinct quantum limits, one related to each of two equivalency classes of the orbifolds $M^{10}\times S^1/Z_2$.
A non-supersymmetric ten-dimensional open string theory is constructed as an orbifold of type I string theory, and as an orientifold of the bosonic type B theory. It is purely bosonic, and cancellation of massless tadpoles requires the gauge group to be SO(32)xSO(32). The spectrum of the theory contains a closed string tachyon, and open string tachyons in the (32,32) multiplet. The D-branes of this theory are analyzed, and it is found that the massless excitations of one of the 1-branes coincide with the world-sheet degrees of freedom of the D=26 bosonic string theory compactified on the SO(32…
We construct a model of M-theory vacua using gauged S-duality and the Chan-Paton symmetries by introducing an infinite number of open string charges. In the Bechi-Rouet-Stora-Tyutin formalism, the local description of the gauged S-duality on its moduli space of vacua is fully determined by one physical state condition on the vacua. We introduce the string probe of the spatial degrees of freedom and define the increment of the cosmic time. The dimensionality of space-time and the gauge group of the low energy effective theory originate in the symmetries (with or without their breakdown) in our …
If one begins with the assertion that the type IIA string compactified on a K3 surface is equivalent to the heterotic string on a four-torus one may try to find a statement about duality in ten dimensions by decompactifying the four-torus. Such a decompactification renders the K3 surface highly singular. The resultant K3 surface may be analyzed in two quite different ways - one of which is natural from the point of view of differential geometry and the other from the point of view of algebraic geometry. We see how the former leads to a "squashed K3 surface" and reproduces the Horava-Witten pic…
We study general black-hole solutions of the low-energy string effective action in arbitrary dimensions using a general metric that can describe them all in a unified way both in the extreme and non-extreme cases. We calculate the mass, temperature and entropy and study which relations amongst the charges and the mass lead to extremality. We find that the temperature always vanishes in the extreme limit and we find that, for a set of n charges (no further reducible by duality) there are 2^{(n-1)} combinations of the charges that imply extremality. Not all of these combinations can be central c…
Following the RG flow of an N=1 quiver gauge theory and applying Seiberg duality whenever necessary defines a duality cascade, that in simple cases has been understood holographically. It has been argued that in certain cases, the dualities will pile up at a certain energy scale called the duality wall, accompanied by a dramatic rise in the number of degrees of freedom. In string theory, this phenomenon is expected to occur for branes at a generic threefold singularity, for which the associated quiver has Lorentzian signature. We here study sequences of Seiberg dualities on branes at the C_3/Z…
In recent work Kachru, Kumar and Silverstein introduced a special class of non-supersymmetric type II string theories in which the cosmological constant vanishes at the first two orders of perturbation theory. Heuristic arguments suggest the cosmological constant may vanish in these theories to all orders in perturbation theory leading to a flat potential for the dilaton. A slight variant of their model can be described in terms of a dual heterotic theory. The dual theory has a non-zero cosmological constant which is non-perturbative in the coupling of the original type II theory. The dual the…
