scholarly journals A NOTE ON EFFECTIVE STRING THEORY

1993 ◽  
Vol 08 (29) ◽  
pp. 2763-2773
Author(s):  
SHYAMOLI CHAUDHURI ◽  
DJORDJE MINIC
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Target Space ◽  
Effective Theory ◽  
Scaling Exponents ◽  
Random Surfaces ◽  
Yang Mills ◽  
Fixed Area ◽  
Effective String Theory

Motivated by the possibility of an effective string description for the ir limit of pure Yang-Mills theory, we present a toy model for an effective theory of random surfaces propagating in a target space of D > 2. We show that the scaling exponents for the fixed area partition function of the theory are apparently well behaved. We make some observations regarding the usefulness of this toy model.

scholarly journals 3D Yang-Mills glueballs vs closed effective strings

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Sergei Dubovsky ◽  
Guzmán Hernández-Chifflet ◽  
Shahrzad Zare
Keyword(s):  
Angular Momentum ◽  
String Theory ◽  
Regge Trajectory ◽  
Effective Theory ◽  
Perturbative Calculation ◽  
Yang Mills ◽  
Quantum Numbers ◽  
Glueball Mass ◽  
Effective String Theory ◽  
Large Angular Momentum

Abstract Recent lattice results strongly support the Axionic String Ansatz (ASA) for quantum numbers of glueballs in 3D Yang-Mills theory. The ASA treats glueballs as closed bosonic strings. The corresponding worldsheet theory is a deformation of the minimal Nambu-Goto theory. In order to understand better the ASA strings and as a first step towards a perturbative calculation of the glueball mass splittings we compare the ASA spectrum to the closed effective string theory. Namely, we model glueballs as excitations around the folded rotating rod solution with a large angular momentum J. The resulting spectrum agrees with the ASA in the regime of validity of the effective theory, i.e., in the vicinity of the leading Regge trajectory. In particular, closed effective string theory correctly predicts that only glueballs of even spin J show up at the leading Regge trajectory. Interestingly though, the closed effective string theory overestimates the number of glueball states far above the leading Regge trajectory.

scholarly journals TWO-DIMENSIONAL YANG-MILLS THEORIES ARE STRING THEORIES

1993 ◽  
Vol 08 (23) ◽  
pp. 2223-2235 ◽  
Author(s):  
STEPHEN G. NACULICH ◽  
HAROLD A. RIGGS ◽  
HOWARD J. SCHNITZER
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Arbitrary Number ◽  
Closed String ◽  
Two Dimensional ◽  
Branched Covers ◽  
Yang Mills ◽  
String Worldsheet ◽  
String Theories

We show that two-dimensional SO (N) and Sp (N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold ℳ can be associated with maps from a string worldsheet onto ℳ. These maps are unbranched and branched covers of ℳ with an arbitrary number of infinitesimal worldsheet cross-caps mapped to points in ℳ. These string theories differ from SU (N) Yang-Mills string theory in that they involve odd powers of 1/N and require both orientable and nonorientable worldsheets.

scholarly journals Localization of the gauged linear sigma model for KK5-branes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yuki Hiraga ◽  
Yuki Sato
Keyword(s):  
Partition Function ◽  
Sigma Model ◽  
Low Energy ◽  
Target Space ◽  
Linear Sigma Model ◽  
Effective Theory ◽  
Coulomb Branch ◽  
World Sheet ◽  
The World ◽  
Gauged Linear Sigma Model

Abstract We study quantum aspects of the target space of the non-linear sigma model, which is a low-energy effective theory of the gauged linear sigma model (GLSM). As such, we especially compute the exact sphere partition function of the GLSM for KK$5$-branes whose background geometry is a Taub–NUT space, using the supersymmetric localization technique on the Coulomb branch. From the sphere partition function, we distill the world-sheet instanton effects. In particular, we show that, concerning the single-centered Taub–NUT space, instanton contributions exist only if the asymptotic radius of the $S^1$ fiber in the Taub–NUT space is zero.

scholarly journals The partition function of interfaces from the Nambu-Goto effective string theory

2006 ◽  
Vol 2006 (02) ◽  
pp. 070-070 ◽  
Author(s):  
Marco Billó ◽  
Michele Caselle ◽  
Livia Ferro
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Effective String Theory

scholarly journals COHOMOLOGICAL FIELD THEORY APPROACH TO MATRIX STRINGS

1999 ◽  
Vol 14 (25) ◽  
pp. 3979-4002 ◽  
Author(s):  
FUMIHIKO SUGINO
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Partition Function ◽  
Three Dimensional ◽  
Exact Result ◽  
Theory Approach ◽  
Two Dimensional ◽  
Yang Mills ◽  
Infrared Limit ◽  
Cohomological Field Theory

In this paper we consider IIA and IIB matrix string theories which are defined by two-dimensional and three-dimensional super Yang–Mills theory with the maximal supersymmetry, respectively. We exactly compute the partition function of both of the theories by mapping to a cohomological field theory. Our result for the IIA matrix string theory coincides with the result obtained in the infrared limit by Kostov and Vanhove, and thus gives a proof of the exact quasiclassics conjectured by them. Further, our result for the IIB matrix string theory coincides with the exact result of IKKT model by Moore, Nekrasov and Shatashvili. It may be an evidence of the equivalence between the two distinct IIB matrix models arising from different roots.

scholarly journals Duality and mock modularity

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Atish Dabholkar ◽  
Pavel Putrov ◽  
Edward Witten
Keyword(s):  
Partition Function ◽  
Elliptic Genus ◽  
Two Dimensions ◽  
Effective Theory ◽  
Coulomb Branch ◽  
Gauge Groups ◽  
Yang Mills ◽  
Holomorphic Anomaly ◽  
Holomorphic Anomaly Equation ◽  
Relevant Field

We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional \mathcal{N} =4𝒩=4 super Yang-Mills theory on \mathbb{CP}^{2}ℂℙ2 for the gauge group SO(3)SO(3) from the path integral of the effective theory on the Coulomb branch. The holomorphic kernel of this equation, which receives contributions only from the instantons, is not modular but ‘mock modular’. The partition function has correct modular properties expected from SS-duality only after including the anomalous nonholomorphic boundary contributions from anti-instantons. Using M-theory duality, we relate this phenomenon to the holomorphic anomaly of the elliptic genus of a two-dimensional noncompact sigma model and compute it independently in two dimensions. The anomaly both in four and in two dimensions can be traced to a topological term in the effective action of six-dimensional (2,0)(2,0) theory on the tensor branch. We consider generalizations to other manifolds and other gauge groups to show that mock modularity is generic and essential for exhibiting duality when the relevant field space is noncompact.

TWO DIMENSIONAL QUANTUM GRAVITY AND STRINGS

1990 ◽  
Vol 05 (10) ◽  
pp. 1833-1859 ◽  
Author(s):  
A.A. TSEYTLIN
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Conformal Factor ◽  
Target Space ◽  
Effective Theory ◽  
Two Dimensional ◽  
Conformal Gauge

We discuss some recent suggestions about a relation between 2-d quantum gravity and string theory. We consider the general 2-d σ model with D-dimensional target space coupled to 2-d quantum gravity and give arguments in favor of the conjecture that the effective theory which describes this system in the conformal gauge may be interpreted as a a model with a D+1-dimensional target space with the conformal factor of the metric playing the role of the D+1 coordinate. The latter σ model must be Weyl invariant while the original one may be arbitrary. The conformal “split” invariance which must be present in the conformal gauge imposes no restrictions on the original σ model couplings, but restricts the additional (D+1-dimensional) couplings which appear in the D+1-dimensional σ model.

scholarly journals Double-Janus linear sigma models and generalized reciprocity for Gauss sums

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ori J. Ganor ◽  
Hao-Yu Sun ◽  
Nesty R. Torres-Chicon
Keyword(s):  
Partition Function ◽  
Berry Phase ◽  
Complex Structure ◽  
Gauss Sums ◽  
The Other ◽  
Target Space ◽  
Mapping Torus ◽  
Yang Mills ◽  
Upper Half Plane ◽  
Linear Sigma Models

Abstract We study the supersymmetric partition function of a 2d linear σ-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d $$ \mathcal{N} $$ N = 4 U(1) Super-Yang-Mills theory compactified on a mapping torus (T2 fibered over S1) times a circle with an SL(2, ℤ) duality wall inserted on S1, but our setup has minimal supersymmetry. The partition function depends on two independent elements of SL(2, ℤ), one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the Landsberg-Schaar relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.

scholarly journals Deconstructing little strings with $\mathcal{N}=1$ gauge theories on ellipsoids

2018 ◽  
Vol 4 (6) ◽  
Author(s):  
Joseph Hayling ◽  
Rodolfo Panerai ◽  
Constantinos Papageorgakis
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Analytic Continuation ◽  
Gauge Theories ◽  
Partition Functions ◽  
Yang Mills ◽  
The Relationship

A formula was recently proposed for the perturbative partition function of certain \mathcal N=1𝒩=1 gauge theories on the round four-sphere, using an analytic-continuation argument in the number of dimensions. These partition functions are not currently accessible via the usual supersymmetric-localisation technique. We provide a natural refinement of this result to the case of the ellipsoid. We then use it to write down the perturbative partition function of an \mathcal N=1𝒩=1 toroidal-quiver theory (a double orbifold of \mathcal N=4𝒩=4 super Yang–Mills) and show that, in the deconstruction limit, it reproduces the zero-winding contributions to the BPS partition function of (1,1) Little String Theory wrapping an emergent torus. We therefore successfully test both the expressions for the \mathcal N=1𝒩=1 partition functions, as well as the relationship between the toroidal-quiver theory and Little String Theory through dimensional deconstruction.

scholarly journals Holographic and localization calculations of boundary F for $$ \mathcal{N} $$ = 4 SUSY Yang-Mills theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Mark Van Raamsdonk ◽  
Chris Waddell
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Partition Function ◽  
Boundary Conditions ◽  
Half Space ◽  
Scale Invariance ◽  
Entanglement Entropy ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Renormalization Group Flows

Abstract $$ \mathcal{N} $$ N = 4 Supersymmetric Yang-Mills (SYM) theory can be defined on a half-space with a variety of boundary conditions preserving scale invariance and half of the original supersymmetry; more general theories with the same symmetry can be obtained by coupling to a 3D SCFT at the boundary. Each of these theories is characterized by a quantity called “boundary F”, conjectured to decrease under boundary renormalization group flows. In this paper, we calculate boundary F for U(N) $$ \mathcal{N} $$ N = 4 SYM theory with the most general half-supersymmetric boundary conditions arising from string theory constructions with D3-branes ending on collections of D5-branes and/or NS5-branes. We first perform the calculation holographically by evaluating the entanglement entropy for a half-ball centered on the boundary using the Ryu-Takayanagi formula in the dual type IIB supergravity solutions. For boundary conditions associated with D3-branes ending on D5 branes only or NS5-branes only, we also calculate boundary F exactly by evaluating the hemisphere partition function using supersymmetric localization. The leading terms at large N in the supergravity and localization results agree exactly as a function of the t’ Hooft coupling λ.

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