CONSISTENCY CONDITION FOR κ-ANOMALIES AND SUPERSPACE CONSTRAINTS IN QUANTUM HETEROTIC SUPERSTRINGS

1989 ◽  
Vol 04 (08) ◽  
pp. 1983-2013 ◽  
Author(s):  
M. TONIN
Keyword(s):  
General Structure ◽  
Consistency Condition ◽  
Quantum Corrections ◽  
World Sheet ◽  
Yang Mills ◽  
The World

In this paper, the quantum heterotic Green and Schwarz superstring in Yang-Mills and curved superspace background is investigated. A consistency condition for the anomalies, allowing to study their general structure, has been obtained. We have found that the anomalies of the κ-symmetry can be absorbed by consistent quantum corrections of torsion and curvatures leading to superspace constraints in agreement with those considered in recent studies on SUGRA-SYM models. Moreover we suggest that the world sheet conformal and Lorentz anomalies vanish if the κ-anomalies are cancelled.

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645040
Author(s):  
Arkady Vainshtein
Keyword(s):  
Sigma Models ◽  
Two Dimensions ◽  
Two Dimensional ◽  
World Sheet ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Straightforward Method ◽  
The World ◽  
Original Formula

We study two-dimensional sigma models where the chiral deformation diminished the original [Formula: see text] supersymmetry to the chiral one, [Formula: see text]. Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional [Formula: see text] theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the [Formula: see text] functions in terms of the anomalous dimensions analogous to the NSVZ [Formula: see text] function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

scholarly journals THE WALL OF THE CAVE

1999 ◽  
Vol 14 (05) ◽  
pp. 645-657 ◽  
Author(s):  
A. M. POLYAKOV
Keyword(s):  
Physical Meaning ◽  
Gauge Fields ◽  
Renormalization Scale ◽  
40Th Anniversary ◽  
World Sheet ◽  
Curved Space ◽  
Yang Mills ◽  
Fifth Dimension ◽  
The World ◽  
Noncritical Strings

In this article old and new relations between gauge fields and strings are discussed. We add new arguments that the Yang–Mills theories must be described by the noncritical strings in the five-dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field. We analyze the meaning of the zigzag symmetry and show that it is likely to be present if there is a minimal supersymmetry on the world sheet. We also present the new string backgrounds which may be relevant for the description of the ordinary bosonic Yang–Mills theories. The article is written on the occasion of the 40th anniversary of the IHES.

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.

Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

1995 ◽  
Vol 73 (5-6) ◽  
pp. 344-348 ◽  
Author(s):  
Yeong-Chuan Kao ◽  
Hsiang-Nan Li
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Landau Gauge ◽  
Quantum Corrections ◽  
Simons Theory ◽  
Loop Correction ◽  
Loop Contribution ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

scholarly journals Stress-energy tensor correlators from the world-sheet

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hanno Bertle ◽  
Andrea Dei ◽  
Matthias R. Gaberdiel
Keyword(s):  
Vertex Operator ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
World Sheet ◽  
Stress Energy ◽  
The World

Abstract The large N limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an sl(2, ℝ) WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective.

scholarly journals THE PROPER TIME FORMALISM, GAUGE INVARIANCE AND THE EFFECTS OF A FINITE WORLD SHEET CUTOFF IN STRING THEORY

1995 ◽  
Vol 10 (31) ◽  
pp. 4501-4519 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Transformation ◽  
Gauge Invariance ◽  
Proper Time ◽  
World Sheet ◽  
Massive Mode ◽  
Yang Mills ◽  
Previous Discussion ◽  
Time Formalism ◽  
Klein Gordon ◽  
Type Interaction

We discuss the issue of going off-shell in the proper time formalism. This is done by keeping a finite world sheet cutoff. We construct one example of an off-shell covariant Klein-Gordon type interaction. For a suitable choice of the gauge transformation of the scalar field, gauge invariance is maintained off-mass-shell. However, at the second order in the gauge field interaction, one finds that [U(1)] gauge invariance is violated due to the finite cutoff. Interestingly, we find, to the lowest order, that by adding a massive mode with appropriate gauge transformation laws to the sigma model background, we can restore gauge invariance. The gauge transformation law is found to be consistent, to the order calculated, with what one expects from the interacting equation of motion of the massive field. We also extend some previous discussion on applying the proper time formalism for propagating gauge particles, to the interacting (i.e. Yang-Mills) case.

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 The World as Quarks, Leptons and Bosons

1976 ◽  
Vol 29 (6) ◽  
pp. 347 ◽  
Author(s):  
M Gell-Mann
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Strong Interactions ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Electromagnetic Interactions ◽  
The World

A descriptive review is given of gauge theories of weak, electromagnetic and strong interactions. The strong interactions are interpreted in terms of an unbroken Yang-Mills gauge theory based on SU(3) colour symmetry of quarks and gluons. The confinement mechanism of quarks, gluons and other nonsinglets is discussed. The unification of the weak and electromagnetic interactions through a broken Yang-Mills gauge theory is described. In total the basic constituents are then the quarks, leptons and gauge bosons.

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