Branes, geometry and N = 1 duality with product gauge groups of SO and Sp

We study N = 1 dualities in four-dimensional supersymmetric gauge theories as the world volume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO(N_c1) × Sp(N_c2) with the superpotential W = TrX⁴ to the case of W = TrX^4(k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO(N_c1) × Sp(N_c2) × SO(N_c3), SO(N_c1) × Sp(N_c2) × SO(N_c3) × Sp(N_c4) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.     

Dyonic membranes

We present dyonic multi-membrane solutions of the N = 2 D = 8 supergravity theory that serves as the effective field theory of the T²-compactified type II superstring theory. The ‘electric’ charge is fractional for generic asymptotic values of an axion field, as for D = 4 dyons. These membrane solutions are supersymmetric, saturate a Bogomolnyi bound, fill out orbits of an subgroup of the type II D = 8 T-duality group, and are non-singular when considered as solutions of T³-compactified D = 11 supergravity. On K₃ compactification to D = 4, the conjectured type II/heterotic equivalence allows the group to be reinterpreted as the S-duality group of the toroidally compactified heterotic string and the dyonic membranes wrapped around homology two-cycles of K₃ as S-duals of perturbative heterotic string states.     

Branes and N = 1 duality in string theory

We propose a construction of dual pairs in four dimensional N = 1 supersymmetric Yang-Mills theory using branes in type IIA string theory.     

0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

Self-dual supergravity from N = 2 strings

A new heterotic N = 2 string with manifest target space supersymmetry is constructed by combining a conventional N = 2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma mode] is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in t', all in superspace. The resulting field equations describe N = 1 self-dual supergravity.     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N_f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2N_f → Sp (2N_f) and SU (N_f → O (N_f), respectively, rather than the symmetry breaking pattern SU (N_f) × SU (N_f) → SU (N_f) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ Λ_QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ 1/L₂ Λ_QCD (wing L the linear size fo the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.     

2D gravity+1D matter

We consider a formulation of nonperturbative two-dimensional quantum gravity coupled to a single bosonic field (d=1 matter). Starting from a matrix realization of the discretized model, we express the continuum theory as a double scaling limit in which the 2D cosmological constant g tends towards a critical value g_c, and the string coupling 1/N→0, with the scaling parameter ∝1n (g-g_c)/(g-g_c)N held fixed. We find that in this formulation logarithmic corrections already present at tree level persist to all higher genus, suggesting a behavior different from the previously considered cases of d<1 matter.     

Geometry of N = 1 dualities in four dimensions

We discuss how N = 1 dualities in four dimensions are geometrically realized by wrapping D-branes about 3-cycles of Calabi-Yau threefolds. In this setup the N = 1 dualities for SU, SO and USp gauge groups with fundamental fields get mapped to statements about the monodromy and relations among 3-cycles of Calabi-Yau threefolds. The connection between the theory and its dual requires passing through configurations which are T-dual to the well-known phenomenon of decay of BPS states in N = 2 field theories in four dimensions. We compare our approach to recent works based on configurations of D-branes in the presence of NS 5-branes and give simple classical geometric derivations of various exotic dynamics involving D-branes ending on NS branes.     

Four-dimensional supersymmetric black holes of type IIA superstring

We systematically construct a large class of four-dimensional supersymmetric black hole solutions of toroidally compactified type IIA superstring theory by explicitly solving the Killing spinor equations. They correspond to orthogonally intersecting configurations in ten dimensions. With the Kaluza-Klein monopole, they are parameterized by four charges and preserve of the N = 8 supersymmetry. We found a simple map to associate each charge with the corresponding Killing spinor constraints. The embedding of the N = 4 supersymmetry of a toroidally compactified heterotic string into the N = 8 supersymmetry of the IIA superstring was explicitly shown. We also found explicitly the configurations with only Ramond-Ramond charges, and those with both Neveu-Schwarz Neveu-Schwarz charges and Ramond-Ramond charges, including the dilaton and the internal metrics. The T-dual of these configurations were shown to satisfy the Killing spinor equations as well.     

Dynamics of N = 2 supersymmetric gauge theories in three dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N _f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.     

New non-Abelian effects on D-branes

We extend the Myers dielectric effect to configurations with angular momentum. The resulting time-dependent N D0 brane bound states can be interpreted as describing rotating fuzzy ellipsoids. A similar solution exists also in the presence of a RR magnetic field, that we study in detail. We show that, for any finite N, above a certain critical angular momentum is energetically more favorable for the bound state system to dissociate into an Abelian configuration of N D0 branes moving independently. We have investigated this problem in the low-energy expansion of the non-Abelian D brane action for generic N. In the case N=2 we find explicit solutions of the full non-Abelian Born–Infeld D brane dynamics, which remarkably have the same structure and confirm the features of the low-energy approximation. We further study D string configurations representing fuzzy funnels deformed by the magnetic field and by the rotational motion.     

Exact monodromy group of N = 2 heterotic superstring

We describe an N = 2 heterotic superstring model of rank 3 which is dual to the type II string compactified on a Calabi-Yau manifold with Betti numbers b_1,1 = 2 and b_1,2 = 86. We show that the exact duality symmetry found from the type II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU(2) super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius.     

通过纠缠交换实现N粒子任意态的概率传态

量子隐形传态的杰出安全特性使其在未来的通讯领域充满潜力.量子力学的不确定性原理和不可克隆定理禁止对量子态进行直接复制,因此,量子隐形传态将量子态划分为经典和量子两部分,信息分别经由经典和量子通道从发送者Alice传递给远方的接收者Bob,根据这两种信息,Bob实行相应操作就可以以一定的几率重建初始传送态.利用一般意义的隐形传态方案,提出一种简便的新方法实现了一个N粒子任意态的概率传态.方法采用N个非最大纠缠的三粒子GHZ态作为量子通道,避免了引入额外的辅助粒子.为了实现传态,Alice将所有粒子分成N份,对第i份的粒子对(i,x_i)实行Bell测量并将结果通过经典通道通知Bob,Bob对粒子(y_i,z_i)进行相应的操作就可以完成第i个粒子信息的传送.当完成N次相似的重复操作后,Bob就可以准确地重建初始传送态.文中以Bell态测量为基本手段,重复的操作同时也降低了实验难度,作为一个特例,文中给出了一个两粒子任意态的传态方案.     

On the string interpretation of M(atrix) theory

It has been proposed recently that, in the framework of M(atrix) theory, = 8 supersymmetric U(N) Yang-Mills theory in 1 + 1 dimensions gives rise to type IIA long string configurations. We point out that the quantum moduli space of SYM_{1 + 1} gives rise to two quantum numbers, which fit very well into the M(atrix) theory. The two quantum numbers become familiar if one switches to a IIB picture, where they represent configurations of D-strings and fundamental strings. We argue that, due to the SL(2,Z) symmetry, of the IIB theory, such quantum numbers must represent configurations that are present also in the IIA framework.     

Non-threshold (F, Dp) bound states

In the previous paper [hep-th/9904112], we argued that there exist BPS bound states of Dp branes carrying certain units of quantized constant electric field for every p (with 1 p 8). Each of these bound states preserves one half of the spacetime supersymmetries. In this paper, we construct these bound state configurations explicitly for 2 p 7 from Schwarz's (m, n)-string or (F, D1) bound state in type IIB string theory by T-dualities along the transverse directions. We calculate the charge per of (p − 1)-dimensional area for F-strings in (F,Dp) and the tension for each of these bound states. The results agree precisely with those obtained previously from the worldvolume study. We study the decoupling limit for the (F, D3) bound state and find that Maldacena's AdS₅/CFT₄ correspondence may hold true even with respect to this bound state but now with an effective string coupling rather than the usual string coupling. This coupling is quantized and can be independent of the usual string coupling in a certain limit.     

Relativistic field-theoretical equations for the three-body multichannel πN and γN scattering reactions and propagator of the Δ-resonance

A new form of the relativistic three-body equations for the coupled πN and γN scattering reactions with three particle final states ππN and γπN is suggested. These equations are derived in the framework of the time-ordered three dimensional field theory. The solutions of the considered equations satisfy the unitarity condition and are exactly gauge invariant. The form of these three-body equations is does not depend on the choice of the model of Lagrangian and is also the same for the formulations with and without quark degrees of freedom.

The effective potentials of the suggested equations are defined by the vertex functions with two on-mass shell particles. It is emphasized that these input vertex functions can be constructed from experimental data. Special attention is given to the construction of the propagator of the Δ-resonance in the framework of the separable πN potential model. The strong dependence of the multichannel πN and γN cross sections on the form of the Δ-resonance propagator[2] is discussed.

The used formulation of the relativistic three-dimensional and three-body equations allows us to overcome a number of approximations which are usually used by practical calculations of the πN and γN scattering reactions.     

Explicit counteraction algorithms in higher dimensions

Using the background field method we construct algorithms for the one-loop counterterms of a field theory in a space-time of dimension 2, 4, 6, 8 or 10. From the d = 6 algorithm we demonstrate the one-loop finiteness of N = 2 supersymmetric Yang-Mills theories and also N = 1 Yang-Mills theory. All other N = 1 Yang-Mills theories + N = 1 matter theories in d = 6 are shown to have a divergent one-loop S-matrix.

We also present partial results for two- and three-loop algorithms in d = 6 and d = 4 respectively.     

Entanglement measures of a new type pseudo-pure state in accelerated frames

In this work we analyze the characteristics of quantum entanglement of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity N_ABI (ρ^TA_ABI) increases with F but decreases with the variable y, while the variation of the negativity N_BIBII(ρ^TA_ABI) is opposite to that of the negativity N_ABI (ρ^TA_ABI). We also study the von Neumann entropies S(ρ_ABI) and S(ρ_BIBII). We find that the S(ρ_ABI) increases with variable y but S(ρ_BIBII) is independent of it. However, both S(ρ_ABI) and S(ρ_BIBII) first decreases with F and then increases with it. The concurrences C(ρ_ABI) and C(ρ_BIBII) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it.     

The quantum mechanics of affine variables

We study the wrapping of N-type IIB Dp-branes on a compact Riemann surface Σ in genus g>1 by means of the Sen–Witten construction, as a superposition of N′-type IIB Dp′-brane/antibrane pairs, with p′>p. A background Neveu–Schwarz field B deforms the commutative C-algebra of functions on Σ to a non-commutative C-algebra. Our construction provides an explicit example of the N′→∞ limit advocated by Bouwknegt-Mathai and Witten in order to deal with twisted K-theory. We provide the necessary elements to formulate M(atrix) theory on this new C-algebra, by explicitly constructing a family of projective C-modules admitting constant-curvature connections. This allows us to define the g>1 analogue of the BPS spectrum of states in g=1, by means of Donaldson’s formulation of the Narasimhan–Seshadri theorem.