scholarly journals Open giant magnons on LLM geometries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
David Berenstein ◽  
Adolfo Holguin
Keyword(s):  
Field Theory ◽  
Angular Momentum ◽  
Dispersion Relation ◽  
Spin Chain ◽  
Radial Direction ◽  
Sigma Model ◽  
Perturbative Expansion ◽  
Additional Information ◽  
Open Strings ◽  
Special Case

Abstract We compute sigma model solutions for rigidly rotating open strings suspended between giant gravitons in general LLM geometries. These solutions are confined to the LLM plane. These all have a dispersion relation for ∆ − J that is consistent with saturation of a BPS bound of the centrally extended spin chain. For the special case of circularly symmetric LLM geometries, we can further evaluate the amount of angular momentum J carried by these strings. This quantity diverges for string configurations that try to move between different “coloring regions” in the LLM plane. All of these quantities have a perturbative expansion in the t’Hooft coupling. For the strings suspended between AdS giants, we can compute in field theory the leading result of J carried by the string via an analytic continuation of the SU(2) result, with the help of the Bethe Ansatz for the SL(2) sector. We thus provide additional information on how the radial direction of AdS arises from (open) spin chain calculations.

Hyper-asymptotic expansions and instantons

2019 ◽  
pp. 471-492
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Asymptotic Expansions ◽  
Perturbative Expansion ◽  
Quantum Field ◽  
Wkb Method ◽  
Additional Information ◽  
Spectral Equation ◽  
Double Well Potential

Chapter 24 examines the topic of hyper–asymptotic expansions and instantons. A number of quantum mechanics and quantum field theory (QFT) examples exhibit degenerate classical minima connected by quantum barrier penetration effects. The analysis of the large order behaviour, based on instanton calculus, shows that the perturbative expansion is not Borel summable, and does not define unique functions. An important issue is then what kind of additional information is required to determine the exact expanded functions. While the QFT examples are complicated, and their study is still at the preliminary stage, in quantum mechanics, in the case of some analytic potentials that have degenerate minima (like the quartic double–well potential), the problem has been completely solved. Some examples are described in Chapter 24. There, the perturbative, complete, hyper–asymptotic expansion exhibits the resurgence property. The perturbative expansion can be related to the calculation of the spectral equation via the complex WKB method.

scholarly journals N-spike string in AdS3 × S1 with mixed flux

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Rashmi R. Nayak ◽  
Priyadarshini Pandit ◽  
Kamal L. Panigrahi
Keyword(s):  
Angular Momentum ◽  
Dispersion Relation ◽  
Sigma Model ◽  
Integrable Models ◽  
Winding Number

Abstract Sigma model in AdS3× S3 background supported by both NS-NS and R-R fluxes is one of the most distinguished integrable models. We study a class of classical string solutions for N-spike strings moving in AdS3× S1 with angular momentum J in S1 ⊂ S5 in the presence of mixed flux. We observe that the addition of angular momentum J or winding number m results in the spikes getting rounded off and not end in cusp. The presence of flux shows no alteration to the rounding-off nature of the spikes. We also consider the large N-limit of N-spike string in AdS3× S1 in the presence of flux and show that the so-called Energy-Spin dispersion relation is analogous to the solution we get for the periodic-spike in AdS3− pp-wave ×S1 background with flux.

Introductory Rotational Dynamics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Angular Momentum ◽  
Angular Displacement ◽  
Rigid Bodies ◽  
Rotational Dynamics ◽  
Circular Motion ◽  
Uniform Rotation ◽  
Chemical Systems ◽  
Inertial Frames ◽  
Rotating Frames ◽  
Special Case

This chapter discusses the importance of circular motion and rotations, whose applications to chemical systems are plentiful. Circular motion is the book’s first example of a special case of motion using the laws developed in previous chapters. The chapter begins with the basic definitions of circular motion; as uniform rotation around a principle axis is much easier to consider, it is the focus of this chapter and is used to develop some key ideas. The chapter discusses angular displacement, angular velocity, angular momentum, torque, rigid bodies, orbital and spin momenta, inertia tensors and non-inertial frames and explores fictitious forces as well as transformations in rotating frames.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals Smooth functorial field theories from B-fields and D-branes

2021 ◽  
Vol 16 (1) ◽  
pp. 75-153
Author(s):  
Severin Bunk ◽  
Konrad Waldorf
Keyword(s):  
Field Theory ◽  
Sigma Models ◽  
Lagrangian Approach ◽  
Field Theories ◽  
Open Strings ◽  
Homotopy Invariant ◽  
Target Manifold ◽  
Definition Of ◽  
Smooth Map

AbstractIn the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth open-closed functorial field theory (FFT) in the sense of Atiyah, Segal, and Stolz–Teichner. We give a detailed construction of this smooth FFT, based on the definition of a suitable smooth bordism category. In this bordism category, all manifolds are equipped with a smooth map to a spacetime target manifold. Further, the object manifolds are allowed to have boundaries; these are the endpoints of open strings stretched between D-branes. The values of our FFT are obtained from the B-field and its D-branes via transgression. Our construction generalises work of Bunke–Turner–Willerton to include open strings. At the same time, it generalises work of Moore–Segal about open-closed TQFTs to include target spaces. We provide a number of further features of our FFT: we show that it depends functorially on the B-field and the D-branes, we show that it is thin homotopy invariant, and we show that it comes equipped with a positive reflection structure in the sense of Freed–Hopkins. Finally, we describe how our construction is related to the classification of open-closed TQFTs obtained by Lauda–Pfeiffer.

A NEW FORMULATION OF QUANTUM FIELD THEORY ON S4

1994 ◽  
Vol 09 (18) ◽  
pp. 3245-3282 ◽  
Author(s):  
B.A. HARRIS ◽  
G.C. JOSHI
Keyword(s):  
Field Theory ◽  
Angular Momentum ◽  
Quantum Gravity ◽  
Momentum Space ◽  
Space Representation ◽  
Fundamental Constants ◽  
Spherical Space ◽  
Recent Developments ◽  
New Formulation ◽  
Constants Of Nature

Recent developments in quantum gravity suggest that wormholes may influence the observed values of the constants of nature. The Euclidean formulation of quantum gravity predicts that wormholes induce a probability distribution in the space of possible fundamental constants. In particular, the effective action on a large spherical space may lead to the vanishing of the cosmological constant and possibly determine the values of other constants of nature. The ability to perform calculations involving interacting quantum fields, particularly non-Abelian models, on a four-sphere is vital if one is to investigate this possibility. In this paper we present a new formulation of field theory on a four-sphere using the angular momentum space representation of SO(5). We give a review of field theory on a sphere and then show how a matrix element prescription in angular momentum space and a new summation technique based on the complex l plane, overcome previous limitations in calculational techniques. The standard one-loop graphs of QED are given as examples.

scholarly journals Different Quantum Field Constructions in the (1/2,0) ⊕ (0,1/2) Representation

1997 ◽  
Vol 12 (36) ◽  
pp. 2741-2748 ◽  
Author(s):  
Valeri V. Dvoeglazov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Neutrino Physics ◽  
Present Situation ◽  
Quantum Field ◽  
Concrete Realization ◽  
Intrinsic Parity ◽  
Special Case

We present another concrete realization of a quantum field theory, envisaged many years ago by Bargmann, Wightman and Wigner. Considering the special case of the (1/2,0)⊕ (0,1/2) field and developing the Majorana–McLennan–Case–Ahluwalia construction for neutrino, we show that fermion and its antifermion can have the same intrinsic parity. The construction can be applied to explain the present situation in neutrino physics.

WARPED COMPACTIFICATION ON SIGMA MODEL, SKYRMIONS IN SIX DIMENSIONS

2007 ◽  
Vol 22 (31) ◽  
pp. 5670-5684 ◽  
Author(s):  
Yuta Kodama ◽  
Kento Kokubu ◽  
Nobuyuki Sawado ◽  
Noriko Shiiki
Keyword(s):  
Field Theory ◽  
Cosmological Constant ◽  
Effective Field Theory ◽  
Extra Dimensions ◽  
Sigma Model ◽  
Effective Field ◽  
Winding Number ◽  
Bulk Cosmological Constant ◽  
Six Dimensions

We construct two distinct brane solutions in six dimensional effective field theory models. The CP 1 sigma model and the baby skyrmion realize warped compactification of the extra dimensions for negative bulk cosmological constant. Higher winding number solutions of the baby skyrmion are also presented.

scholarly journals T-folds as Poisson–Lie plurals

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Ladislav Hlavatý ◽  
Ivo Petr
Keyword(s):  
Field Theory ◽  
Double Field Theory ◽  
Bianchi Cosmologies ◽  
Special Case

AbstractIn previous papers we have presented many purely bosonic solutions of Generalized Supergravity Equations obtained by Poisson–Lie T-duality and plurality of flat and Bianchi cosmologies. In this paper we focus on their compactifications and identify solutions that can be interpreted as T-folds. To recognize T-folds we adopt the language of Double Field Theory and discuss how Poisson–Lie T-duality/plurality fits into this framework. As a special case we confirm that all non-Abelian T-duals can be compactified as T-folds.

Chiral strings, topological branes, and a generalised Weyl-invariance

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1950031 ◽  
Author(s):  
Alex S. Arvanitakis
Keyword(s):  
Field Theory ◽  
Sigma Model ◽  
Space Time ◽  
Symplectic Space ◽  
Topological Field Theory ◽  
Brst Operator ◽  
Weyl Invariance ◽  
Fixed Action ◽  
Twistor Strings ◽  
Topological Field

We introduce a sigma model Lagrangian generalising a number of new and old models which can be thought of as chiral, including the Schild string, ambitwistor strings, and the recently introduced tensionless AdS twistor strings. This “chiral sigma model” describes maps from a [Formula: see text]-brane worldvolume into a symplectic space and is manifestly invariant under diffeomorphisms as well as under a “generalised Weyl invariance” acting on space–time coordinates and worldvolume fields simultaneously. Construction of the Batalin–Vilkovisky master action leads to a BRST operator under which the gauge-fixed action is BRST-exact; we discuss whether this implies that the chiral brane sigma model defines a topological field theory.

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