arXiv subjects

N. A. Obers

Publications and source records attributed to N. A. Obers.

At least 37 records · Page 2Linked to original sources

arXiv2000

Hagedorn Behavior of Little String Theories

We examine the Hagedorn behavior of little string theory using its conjectured duality with near-horizon NS5-branes. In particular, by studying the string-corrected NS5-brane supergravity solution, it is shown that tree-level corrections to the temperature vanish, while the leading one-loop string correction generates the correct temperature dependence of the entropy near the Hagedorn temperature. Finally, the Hagedorn behavior of ODp-brane theories, which are deformed versions of little string theory, is considered via their supergravity duals.

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arXiv2000

Exact thresholds and instanton effects in D=3 string theories

Three-dimensional string theories with 16 supersymmetries are believed to possess a non-perturbative U-duality symmetry $SO(8,24,\Zint)$. By covariantizing the heterotic one-loop amplitude under U-duality, we propose an exact expression for the $(\partial ϕ)^4$ amplitude, that reproduces known perturbative limits. The weak-coupling expansion in either of the heterotic, type II or type I descriptions exhibits the well-known instanton effects, plus new contributions peculiar to three-dimensional theories, including the Kaluza-Klein 5-brane, for which we extract the summation measure. This letter is a post-scriptum to hepth/0001083.

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arXiv2000

Hagedorn Behaviour of Little String Theory from String Corrections to NS5-Branes

Following the conjectured duality between near-horizon NS5-branes and little string theory, the string-corrected thermodynamics of near-horizon NS5-branes is studied and found to agree with the statistical thermodynamics of a 5+1 dimensional supersymmetric string theory near the Hagedorn temperature. Specifically, tree-level corrections to the temperature are argued to vanish, in accordance with the duality, while the one-loop string correction to the NS5-brane thermodynamics is shown to generate the correct temperature dependence of the entropy.

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arXiv2000

Phase Structure of Non-Commutative Field Theories and Spinning Brane Bound States

General spinning brane bound states are constructed, along with their near-horizon limits which are relevant as dual descriptions of non-commutative field theories. For the spinning D-brane world volume theories with a B-field a general analysis of the gauge coupling phase structure is given, exhibiting various novel features, already at the level of zero angular momenta. We show that the thermodynamics is equivalent to the commutative case at large N and we discuss the possibility and consequences of finite N. As an application of the general analysis, the range of validity of the thermodynamics for the NCSYM is discussed. In view of the recently conjectured existence of a 7-dimensional NCSYM, the thermodynamics of the spinning D6-brane theory, for which a stable region can be found, is presented in detail. Corresponding results for the spinning M5-M2 brane bound state, including the near-horizon limit and thermodynamics, are given as well.

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arXiv2000

Eisenstein Series in String Theory

We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are manifestly invariant modular functions on the symmetric space K\G(R) of non-compact type, with K the maximal compact subgroup of G(R). In particular, we show how Eisenstein series of the T-duality group SO(d,d,Z) can be used to represent one- and g-loop amplitudes in compactified string theory. We also obtain their non-perturbative extensions in terms of the Eisenstein series of the U-duality group E_{d+1(d+1)}(Z).

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arXiv2000

Thermodynamics of Field Theories from Spinning Branes

We discuss general spinning p-branes of string and M-theory and use their thermodynamics along with the correspondence between near-horizon brane solutions and field theories with 16 supercharges to describe the thermodynamic behavior of these theories in the presence of voltages under the R-symmetry. The thermodynamics is used to provide two pieces of evidence in favor of a smooth interpolation function between the free energy at weak and strong coupling of the field theory. (i) A computation of the boundaries of stability shows that for the D2, D3, D4, M2 and M5-branes the critical values of Omega/T in the two limits are remarkably close and (ii) The tree-level R^4 corrections to the spinning D3-brane generate a decrease in the free energy at strong coupling towards the weak coupling result. We also comment on the generalization to spinning brane bound states and their thermodynamics, which are relevant for non-commutative field theories.

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arXiv2000

Heterotic/Type II Triality and Instantons on $K_3$

A detailed understanding of instanton effects for half-BPS couplings is pursued in theories with 16 supersymmetries. In particular, we investigate the duality between heterotic string on $T^4$ and type IIA on $K_3$ at the $T^4/Z_2$ orbifold point, as well as their higher and lower dimensional versions. We present a remarkably clean quantitative test of the duality at the level of $F^4$ couplings, by completely matching a purely one-loop heterotic amplitude to a purely tree-level type II result. The triality of SO(4,4) and several other miracles are shown to be crucial for the duality to hold. Exact non-perturbative new results for type I', F on $K_3$, M on $K_3$, and IIB on $K_3$ are found, and the general form of D-instanton contributions in type IIA or B on $T^4/Z_2$ is obtained. We also analyze the NS5-brane contributions in type II on $K_3\times T^2$, and predict the value $μ(N)=\sum_{d|N} (1/d^3)$ for the bulk contribution to the index of the NS5-brane world-volume theory on $K_3 \times T^2$.

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arXiv2000

Thermodynamics of Spinning Branes and their Dual Field Theories

We present a general analysis of the thermodynamics of spinning black p-branes of string and M-theory. This is carried out both for the asymptotically-flat and near-horizon case, with emphasis on the latter. In particular, we use the conjectured correspondence between the near-horizon brane solutions and field theories with 16 supercharges in various dimensions to describe the thermodynamic behavior of these field theories in the presence of voltages under the R-symmetry. Boundaries of stability are computed for all spinning branes both in the grand canonical and canonical ensemble, and the effect of multiple angular momenta is considered. A recently proposed regularization of the field theory is used to compute the corresponding boundaries of stability at weak coupling. For the D2, D3, D4, M2 and M5-branes the critical values of Omega/T in the weak and strong coupling limit are remarkably close. Finally, we also show that for the spinning D3-brane the tree level R^4 correction supports the conjecture of a smooth interpolating function between the free energy at weak and strong coupling.

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arXiv1999

U-duality and M-Theory

This work is intended as a pedagogical introduction to M-theory and to its maximally supersymmetric toroidal compactifications, in the frameworks of 11D supergravity, type II string theory and M(atrix) theory. U-duality is used as the main tool and guideline in uncovering the spectrum of BPS states. We review the 11D supergravity algebra and elementary 1/2-BPS solutions, discuss T-duality in the perturbative and non-perturbative sectors from an algebraic point of view, and apply the same tools to the analysis of U-duality at the level of the effective action and the BPS spectrum, with a particular emphasis on Weyl and Borel generators. We derive the U-duality multiplets of BPS particles and strings, U-duality invariant mass formulae for 1/2- and 1/4-BPS states for general toroidal compactifications on skew tori with gauge backgrounds, and U-duality multiplets of constraints for states to preserve a given fraction of supersymmetry. A number of mysterious states are encountered in D<=3, whose existence is implied by T-duality and 11D Lorentz invariance. We then move to the M(atrix) theory point of view, give an introduction to Discrete Light Cone Quantization (DLCQ) in general and DLCQ of M-theory in particular. We discuss the realization of U-duality as electric-magnetic dualities of the Matrix gauge theory, display the Matrix gauge theory BPS spectrum in detail, and discuss the conjectured extended U-duality group in this scheme.

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arXiv1998

U-duality and M-theory, an algebraic approach

Based on our work hep-th/9809039, we discuss how U-duality arises as an exact symmetry of M-theory from T-duality and 11D diffeomorphism invariance. A set of Weyl generators are shown to realize the Weyl group of SO(d,d,Z) and E_{d(d)}(Z), while Borel generators extend these finite groups into the full T- and U-duality groups. We discuss how the BPS states fall into various representations, and obtain duality invariant mass formulae, relevant for the computation of exact string amplitudes. The realization of U-duality symmetry in Matrix gauge theory is also considered.

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arXiv1998

M-Theory and U-duality on T^d with Gauge Backgrounds

The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing non-rectangular tori with expectation values of the gauge fields. We construct an E_d(Z) U-duality invariant mass formula incorporating non-vanishing gauge backgrounds of the M-theory three-form C. We interpret this mass formula from the point of view of the Matrix gauge theory, and identify the coupling of the three-form to the gauge theory as a topological theta term, in agreement with earlier conjectures. We give a derivation of this fact from D-brane analysis, and obtain the Matrix gauge theory description of other gauge backgrounds allowed by the Discrete Light-Cone Quantization. We further show that the conjectured extended U-duality symmetry of Matrix theory on T^d in the Discrete Light-Cone Quantization has an implementation as an action of E_{d+1}(Z) on the BPS spectrum. Some implications for the proper interpretation of the rank N of the Matrix gauge theory are discussed.

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arXiv1997

Heterotic / type I duality and D-brane instantons

We study heterotic/type I duality in d=8,9 uncompactified dimensions. We consider the special (``BPS saturated'') F^4 and R^4 terms in the effective one-loop heterotic action, which are expected to be non-perturbatively exact. Under the standard duality map these translate to tree-level, perturbative and non-perturbative contributions on the type I side. We check agreement with the one-loop open string calculation, and discuss the higher-order perturbative contributions, which arise because of the mild non-holomorphicities of the heterotic elliptic genus. We put the heterotic world-sheet instanton corrections in a form that can be motivated as arising from a D-brane instanton calculation on the type-I side.

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arXiv1997

Heterotic/Type-I Duality in D<10 Dimensions, Threshold Corrections and D-Instantons

We continue our study of heterotic/type-I duality in D<10 dimensions. We consider the heterotic and type-I theories compactified on tori to lower dimensions. We calculate the special (``BPS saturated'') F^4 and R^4 terms in the effective one-loop heterotic action. These terms are expected to be non-perturbatively exact for D>4. The heterotic result is compared with the associated type-I result. In D<9 dimensions, the type-I theory has instanton corrections due to D1 instantons. In D=8 we use heterotic-type I duality to give a simple prescription of the D-instanton calculation on the type I side. We allow arbitrary Wilson lines and show that the D1-instanton determinant is the affine character-valued elliptic genus evaluated at the induced complex structure of the D1-brane world-volume. The instanton result has an expansion in terms of Hecke operators that suggest an interpretation in terms of an SO(N) matrix model of the D1-brane. The total result can be written in terms of generalized prepotentials revealing an underlying holomorphic structure. In D<8 we calculate again the heterotic perturbative thresholds and show that they agree with the D1-instanton calculation using the rules derived in D=8.

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arXiv1997

R^2 Corrections and Non-perturbative Dualities of N=4 String ground states

We compute and analyse a variety of four-derivative gravitational terms in the effective action of six- and four-dimensional type II string ground states with N=4 supersymmetry. In six dimensions, we compute the relevant perturbative corrections for the type II string compactified on K3. In four dimensions we do analogous computations for several models with (4,0) and (2,2) supersymmetry. Such ground states are related by heterotic-type II duality or type II-type II U-duality. Perturbative computations in one member of a dual pair give a non-perturbative result in the other member. In particular, the exact CP-even R^2 coupling on the (2,2) side reproduces the tree-level term plus NS 5-brane instanton contributions on the (4,0) side. On the other hand, the exact CP-odd coupling yields the one-loop axionic interaction a.R\wedge R together with a similar instanton sum. In a subset of models, the expected breaking of the SL(2,Z)_S S-duality symmetry to a Γ(2)_S subgroup is observed on the non-perturbative thresholds. Moreover, we present a duality chain that provides evidence for the existence of heterotic N=4 models in which N=8 supersymmetry appears at strong coupling.

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arXiv1996

New Semiclassical Nonabelian Vertex Operators for Chiral and Nonchiral WZW Theory

We supplement the discussion of Moore and Reshetikhin and others by finding new semiclassical nonabelian vertex operators for the chiral, antichiral and nonchiral primary fields of WZW theory. These new nonabelian vertex operators are the natural generalization of the familiar abelian vertex operators: They involve only the representation matrices of Lie $g$, the currents of affine $(g \times g)$ and certain chiral and antichiral zero modes, and they reduce to the abelian vertex operators in the limit of abelian algebras. Using the new constructions, we also discuss semiclassical operator product expansions, braid relations and relations to the known form of the semiclassical affine-Sugawara conformal blocks.

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arXiv1996

Semi-Classical Blocks and Correlators in Rational and Irrational Conformal Field Theory

The generalized Knizhnik-Zamolodchikov equations of irrational conformal field theory provide a uniform description of rational and irrational conformal field theory. Starting from the known high-level solution of these equations, we first construct the high-level conformal blocks and correlators of all the affine-Sugawara and coset constructions on simple g. Using intuition gained from these cases, we then identify a simple class of irrational processes whose high-level blocks and correlators we are also able to construct.

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arXiv1994

Plane Gravitational Waves in String Theory

We analyze the coset model $(E_2^c \ti E_2^c)/E_2^c$ and construct a class of exact string vacua which describe plane gravitational waves and their duals, generalizing the plane wave background found by Nappi and Witten. In particular, the vector gauging describes a two-parameter family of singular geometries with two isometries, which is dual to plane gravitational waves. In addition, there is a mixed vector-axial gauging which describes a one-parameter family of plane waves with five isometries. These two backgrounds are related by a duality transformation which generalizes the known axial-vector duality for abelian subgroups.

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arXiv1993

Flat Connections and Non-Local Conserved Quantities in Irrational Conformal Field Theory

Irrational conformal field theory (ICFT) includes rational conformal field theory as a small subspace, and the affine-Virasoro Ward identities describe the biconformal correlators of ICFT. We reformulate the Ward identities as an equivalent linear partial differential system with flat connections and new non-local conserved quantities. As examples of the formulation, we solve the system of flat connections for the coset correlators, the correlators of the affine-Sugawara nests and the high-level $n$-point correlators of ICFT.

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