scholarly journals STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE

1999 ◽  
Vol 14 (28) ◽  
pp. 4501-4517 ◽  
Author(s):  
FEDELE LIZZI
Keyword(s):  
String Theory ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Low Energy ◽  
Target Space ◽  
World Sheet ◽  
Crucial Point ◽  
Spectral Action ◽  
Energy Eigenvalues ◽  
The World

We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

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 Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

scholarly journals ON HIGHER-SPIN GENERALIZATIONS OF STRING THEORY

1994 ◽  
Vol 09 (09) ◽  
pp. 1527-1543 ◽  
Author(s):  
H. LU ◽  
C. N. POPE ◽  
X. J. WANG
Keyword(s):  
String Theory ◽  
Gauge Field ◽  
Virasoro Algebra ◽  
Two Dimensional ◽  
Minimal Models ◽  
World Sheet ◽  
The World ◽  
Higher Spin ◽  
String Theories

We construct BRST operators for certain higher-spin extensions of the Virasoro algebra, in which there is a spin-s gauge field on the world sheet, as well as the spin-2 gauge field corrresponding to the two-dimensional metric. We use these BRST operators to study the physical states of the associated string theories, and show how they are related to certain minimal models.

VORTICES IN HIGH-TEMPERATURE STRING THEORY

1989 ◽  
Vol 04 (11) ◽  
pp. 1063-1067 ◽  
Author(s):  
G. CHAPLINE ◽  
F.R. KLINKHAMER
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
High Temperature ◽  
String Theory ◽  
High Temperatures ◽  
World Sheet ◽  
Genus Zero ◽  
Mass Gap ◽  
The World

We discuss the role of XY-like vortices on the world-sheet for the free energy of strings at high temperatures. There is a Kosterlitz-Thouless phase transition at the Hagedorn temperature, above which the vortices contribute to the free energy in genus zero and generate a mass gap. We speculate that high-temperature “string” theory could be essentially discrete.

scholarly journals Spectral action and the electroweak θ-terms for the Standard Model without fermion doubling

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
A. Bochniak ◽  
A. Sitarz ◽  
P. Zalecki
Keyword(s):  
Standard Model ◽  
Symmetry Breaking ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Gauge Fields ◽  
Wick Rotation ◽  
Spectral Action ◽  
Geometry Model ◽  
The Standard Model ◽  
Cp Symmetry

Abstract We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry breaking, has the Dirac operator that is not of the product type. Using Wick rotation we derive explicitly the Lagrangian of the model from the spectral action for a flat metric, demonstrating the appearance of the topological θ-terms for the electroweak gauge fields.

scholarly journals The physical states of the Hybrid Formalism

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Matthias R. Gaberdiel ◽  
Kiarash Naderi
Keyword(s):  
String Theory ◽  
Free Field ◽  
Vertex Operators ◽  
World Sheet ◽  
Brst Cohomology ◽  
The World ◽  
The Way

Abstract String theory on AdS3 × S3 × $$ \mathbbm{T} $$ T 4 with one unit (k = 1) of NS-NS flux is considered in the hybrid formalism of Berkovits, Vafa & Witten (BVW). Using the free field realisation of the world-sheet theory at k = 1, we identify explicitly the BRST cohomology classes corresponding to some of the low-lying states of the dual CFT. In particular, we do this for the $$ \mathcal{N} $$ N = 4 superconformal generators of the symmetric orbifold theory, and we confirm these identifications by showing that the worldsheet correlators reproduce the expected dual CFT answer. Along the way we note that the physical vertex operators on the worldsheet have a simpler form if one works with a different, but equivalent, choice for the BRST operators relative to BVW.

scholarly journals ON THE EVALUATION OF COMPTON SCATTERING AMPLITUDES IN STRING THEORY

1998 ◽  
Vol 13 (27) ◽  
pp. 4717-4757 ◽  
Author(s):  
ANDREA PASQUINUCCI ◽  
MICHELA PETRINI
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Moduli Space ◽  
Modular Forms ◽  
String Model ◽  
World Sheet ◽  
Electron Positron ◽  
The World ◽  
Spin Fields ◽  
Compton Amplitude

We consider the Compton amplitude for the scattering of a photon and an (massless) "electron/positron" at one loop (i.e. genus 1) in a four-dimensional fermionic heterotic string model. Starting from the bosonization of the world sheet fermions needed to explicitly construct the spin fields representing the space–time fermions, we present all the steps of the computation which leads to the explicit form of the amplitude as an integral of modular forms over the moduli space.

GAUGE-COVARIANT WESS-ZUMINO ACTIONS FOR SUPER p-BRANES IN SUPERSPACE

1992 ◽  
Vol 07 (10) ◽  
pp. 2153-2173 ◽  
Author(s):  
E.A. IVANOV ◽  
A.A. KAPUSTNIKOV
Keyword(s):  
World Line ◽  
Soliton Solutions ◽  
Coupling Constants ◽  
Target Space ◽  
Field Theories ◽  
World Sheet ◽  
Type Representation ◽  
Superconformal Symmetry ◽  
The World ◽  
Simple Action

We present a general method of constructing manifestly world-volume supersymmetric actions of super p-branes, starting from some higher-dimensional field theories in which the partial breaking of global supersymmetry (PBGS) comes about. Our approach is based upon a substitution of the superspace coordinates which relates linear and nonlinear realizations of PBGS. As instructive examples we consider the massive d=2 superparticle (p=0) and d=4 superstring (p=1). The relevant world-line and world-sheet superfied actions naturally appear as a long-wavelength limit of the superfield actions of some two- and four-dimensional supersymmetric field theories possessing topologically nontrivial soliton solutions. The corresponding topological charges prove to enter the super p-brane actions as the coupling constants. We also give a new general Wess-Zumino-type representation of the d=2 superparticle action via the world-line superfields. It respects invariances both under the target space Poincaré supersymmetry and the gauge group of general reparametrizations of the world-line superspace. In one gauge, it is reduced to the standard PBGS form while in another, it gives rise to a very simple action which displays manifest world-line superconformal symmetry and is directly related to the familiar component action of the superparticle. The fermionic κ-symmetry of the latter can be identified with the odd sector of superconformal symmetry. This identity suggests a simple recipe for building higher-order κ-invariant corrections to the minimal superparticle action.

scholarly journals String theory and the CPT theorem on the world-sheet

1997 ◽  
Vol 485 (1-2) ◽  
pp. 241-271 ◽  
Author(s):  
Andrea Pasquinucci ◽  
Kaj Roland
Keyword(s):  
String Theory ◽  
World Sheet ◽  
The World ◽  
Cpt Theorem
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