COUPLING THE WESS-ZUMINO-WITTEN MODEL TO YANG-MILLS FIELDS

1991 ◽  
Vol 06 (11) ◽  
pp. 969-976 ◽  
Author(s):  
C.M. HULL ◽  
B. SPENCE
Keyword(s):  
Effective Action ◽  
Dimensional Space ◽  
Low Energy ◽  
Field Theories ◽  
Gauge Fields ◽  
Conformal Field Theories ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field

The coupling of the 2n-dimensional Wess-Zumino-Witten action to gauge fields is discussed and a simple manifestly gauge-invariant form of the gauged Wess-Zumino term is found which is an integral over a (2n+1)-dimensional space whose boundary is space-time. In two and four dimensions, our actions give simple forms for the action describing coset conformal field theories and the low-energy QCD effective action, respectively.

scholarly journals ON THE CONFORMAL ANOMALY FROM HIGHER DERIVATIVE GRAVITY IN AdS/CFT CORRESPONDENCE

2000 ◽  
Vol 15 (03) ◽  
pp. 413-428 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Effective Action ◽  
Einstein Gravity ◽  
Low Energy ◽  
Field Theories ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Yang Mills ◽  
Conformal Field ◽  
Higher Derivative

We follow Witten's proposal1 in the calculation of conformal anomaly from (d + 1)-dimensional higher derivative gravity via AdS/CFT correspondence. It is assumed that some d-dimensional conformal field theories have a description in terms of above (d + 1)-dimensional higher derivative gravity which includes not only the Einstein term and cosmological constant but also curvature squared terms. The explicit expression for two-dimensional and four-dimensional anomalies is found, it contains higher derivative corrections. In particular, it is shown that not only Einstein gravity but also theory with the Lagrangian L =aR2 + bRμνRμν + Λ (even when a=0 or b=0) is five-dimensional bulk theory for [Formula: see text] super-Yang–Mills theory in AdS/CFT correspondence. Similarly, the d + 1 = 3 theory with (or without) Einstein term may describe d = 2 scalar or spinor CFT's. That gives new versions of bulk side which may be useful in different aspects. As application of our general formalism we find next-to-leading corrections to the conformal anomaly of [Formula: see text] supersymmetric theory from d = 5 AdS higher derivative gravity (low energy string effective action).

scholarly journals Instantons beyond topological theory. I

2011 ◽  
Vol 10 (3) ◽  
pp. 463-565 ◽  
Author(s):  
E. Frenkel ◽  
A. Losev ◽  
N. Nekrasov
Keyword(s):  
Correlation Functions ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Conformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Mechanical Models ◽  
Perturbative Corrections

AbstractMany quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyse the corresponding models as full quantum field theories, beyond their topological sector. We show that the correlation functions of all, not only topological (or BPS), observables may be studied explicitly in these models, and the spectrum may be computed exactly. An interesting feature is that the Hamiltonian is not always diagonalizable, but may have Jordan blocks, which leads to the appearance of logarithms in the correlation functions. We also find that in the models defined on Kähler manifolds the space of states exhibits holomorphic factorization. We conclude that in dimensions two and four our theories are logarithmic conformal field theories.In Part I we describe the class of models under study and present our results in the case of one-dimensional (quantum mechanical) models, which is quite representative and at the same time simple enough to analyse explicitly. Part II will be devoted to supersymmetric two-dimensional sigma models and four-dimensional Yang–Mills theory. In Part III we will discuss non-supersymmetric models.

scholarly journals HOPF SOLITON SOLUTIONS FROM LOW ENERGY EFFECTIVE ACTION OF SU(2) YANG–MILLS THEORY

2006 ◽  
Vol 21 (15) ◽  
pp. 1189-1202 ◽  
Author(s):  
NOBUYUKI SAWADO ◽  
NORIKO SHIIKI ◽  
SHINGO TANAKA
Keyword(s):  
Fourth Order ◽  
Effective Action ◽  
Dimensional Space ◽  
Soliton Solutions ◽  
Low Energy ◽  
Effective Theory ◽  
Second Derivative ◽  
Yang Mills ◽  
Extended Action ◽  
Derivative Term

The Skyrme–Faddeev–Niemi (SFN) model which is an O(3) σ-model in three-dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang–Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang–Mills theory recovers the SFN in the infrared region. However, the theory contains another fourth-order term which destabilizes soliton solutions. We find the stable soliton solutions in this extended action, introducing a second derivative term as a stabilizer. A perturbative technique for the second derivative term is applied to exclude (or reduce) the ill behavior of the action. A new topological energy bound formula is inferred for the action.

scholarly journals Boundary conformal field theory at large charge

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Gabriel Cuomo ◽  
Márk Mezei ◽  
Avia Raviv-Moshe
Keyword(s):  
Field Theory ◽  
Background Field ◽  
Effective Field ◽  
Three Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Fisher Model ◽  
Large Charge

Abstract We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between the scaling dimension of the lowest dimensional CFT and BCFT charged operators to leading order in the charge. We also construct the superfluid effective field theory for theories with boundaries and use it to systematically calculate the BCFT spectrum in a systematic expansion. We verify explicitly many of the predictions from the EFT analysis in concrete examples including the classical conformal scalar field with a |ϕ|6 interaction in three dimensions and the O(2) Wilson-Fisher model near four dimensions in the presence of boundaries. In the appendices we additionally discuss a systematic background field approach towards Ward identities in general boundary and defect conformal field theories, and clarify its relation with Noether’s theorem in perturbative theories.

scholarly journals On conformal field theories in four dimensions

1998 ◽  
Vol 533 (1-3) ◽  
pp. 199-209 ◽  
Author(s):  
Albion Lawrence ◽  
Nikita Nekrasov ◽  
Cumrun Vafa
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field

scholarly journals Five-dimensional non-Lorentzian conformal field theories and their relation to six-dimensions

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
N. Lambert ◽  
A. Lipstein ◽  
R. Mouland ◽  
P. Richmond
Keyword(s):  
Correlation Functions ◽  
Conformal Symmetry ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Dimensional Theory ◽  
Superconformal Field Theories ◽  
Yang Mills ◽  
Conformal Field ◽  
Instanton Number ◽  
Do So

Abstract We study correlation functions in five-dimensional non-Lorentzian theories with an SU(1, 3) conformal symmetry. Examples of such theories have recently been obtained as Ω-deformed Yang-Mills Lagrangians arising from a null reduction of six-dimensional superconformal field theories on a conformally compactified Minkowski space. The correlators exhibit a rich structure with many novel properties compared to conventional correlators in Lorentzian conformal field theories. Moreover, identifying the instanton number with the Fourier mode number of the dimensional reduction offers a hope to formulate six-dimensional conformal field theories in terms of five-dimensional Lagrangian theories. To this end we show that the Fourier decompositions of six-dimensional correlation functions solve the Ward identities of the SU(1, 3) symmetry, although more general solutions are possible. Conversely we illustrate how one can reconstruct six-dimensional correlation functions from those of a five-dimensional theory, and do so explicitly at 2- and 3-points. We also show that, in a suitable decompactification limit Ω → 0, the correlation functions become those of the DLCQ description.

4-D SELF-DUAL INSTANTONS FROM 2-D SIGMA MODEL

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 781-789 ◽  
Author(s):  
Q-HAN PARK
Keyword(s):  
Sigma Model ◽  
Field Theories ◽  
Maxwell System ◽  
Conformal Field Theories ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Conformal Field ◽  
Integrable Deformation ◽  
Large N ◽  
Higher Dimensional

4-d self-dual gravity and Yang-Mills theories are identified with 2-d sigma models taking values in infinite dimensional groups. This allows us to view 4-d self-dual theories as "large N limits" of 2-d conformal field theories. We also find a possible "integrable deformation" of 4-d self-dual gravity leading to the Einstein-Maxwell system and discuss its implication in the context of higher dimensional integrability.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

scholarly journals New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
V. A. Ivanovskiy
Keyword(s):  
Effective Action ◽  
Harmonic Superspace ◽  
Four Dimensions ◽  
Yang Mills ◽  
Convenient Tool ◽  
Leading Term

Abstract We develop a novel bi-harmonic $$ \mathcal{N} $$ N = 4 superspace formulation of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $$ \mathcal{N} $$ N = 4 SYM superfield constraints are solved in terms of on-shell $$ \mathcal{N} $$ N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $$ \mathcal{N} $$ N = 4 supersymmetric invariants and further rewriting them in $$ \mathcal{N} $$ N = 2 harmonic superspace. In particular, we present $$ \mathcal{N} $$ N = 4 superfield form of the leading term in the $$ \mathcal{N} $$ N = 4 SYM effective action which was known previously in $$ \mathcal{N} $$ N = 2 superspace formulation.

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