scholarly journals PREPOTENTIALS, BILINEAR FORMS ON PERIODS AND ENHANCED GAUGE SYMMETRIES IN TYPE II STRINGS

1999 ◽  
Vol 14 (08) ◽  
pp. 1177-1203 ◽  
Author(s):  
TAKAHIRO MASUDA ◽  
HISAO SUZUKI
Keyword(s):  
Gauge Symmetry ◽  
Bilinear Form ◽  
Explicit Construction ◽  
Bilinear Forms ◽  
Type Ii ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
The One ◽  
Flat Coordinates

We construct a bilinear form on the periods of Calabi–Yau spaces. This is used to obtain the prepotentials around conifold singularities in type II strings compactified on Calabi–Yau space. Explicit construction of the bilinear forms is achieved for the one-modulus models as well as two-modulus models with K3 fibrations where the enhanced gauge symmetry is known to be observed at the conifold locus. We also show how these bilinear forms are related with the existence of flat coordinates. We list the resulting prepotentials in two-modulus models around the conifold locus, which contains α′ corrections of 4D N=2 SUSY SU(2) Yang–Mills theory as the stringy effect.

Symmetries

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
General Relativity ◽  
Gauge Symmetry ◽  
Laws Of Nature ◽  
Fundamental Property ◽  
Internal Symmetry ◽  
Classical Physics ◽  
Yang Mills ◽  
Electromagnetic Interactions ◽  
Gauge Symmetries ◽  
Euclidian Geometry

The concept of symmetry plays a central role in our understanding of the fundamental laws of Nature. Through a deep mathematical theorem due to A.E. Noether, all conservation laws of classical physics are related to symmetries. In this chapter we start from the intuitively obvious notions of translation and rotation symmetries which are part of the axioms of Euclidian geometry. Following W. Heisenberg, we introduce the idea of isospin as a first example of an internal symmetry. A further abstraction leads to the concept of a global versus local, or gauge symmetry, which is a fundamental property of General Relativity. Combining the notions of internal and gauge symmetries we obtain the Yang-Mills theory which describes all fundamental interactions among elementary particles. A more technical part, which relates a gauge symmetry of the Schrödinger equation of quantum mechanics to the electromagnetic interactions, is presented in a separate section and its understanding is not required for the rest of the book.

scholarly journals EXACTLY SOLVABLE POINTS IN THE MODULI SPACE OF HETEROTIC N=2 STRINGS

1996 ◽  
Vol 11 (18) ◽  
pp. 1475-1487 ◽  
Author(s):  
RALPH BLUMENHAGEN ◽  
ANDREAS WIßKIRCHEN
Keyword(s):  
Vector Bundle ◽  
Gauge Symmetry ◽  
Gauge Group ◽  
Moduli Space ◽  
Type Ii ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Gauge Symmetries ◽  
Exactly Solvable ◽  
Solvable Points

We investigate the subset of exactly solvable (0, 4) worldsheet supersymmetric string vacua contained in a recent class of Gepner-like (0, 2) superconformal models. The identification of these models with certain points of enhanced gauge symmetry on K3×T2 can be achieved completely. Furthermore, we extend the construction of in general (0, 2) supersymmetric exactly solvable models to the case where also a nontrivial part of the vector bundle is embedded into the hidden E8 gauge group. For some examples we explicitly calculate the enhanced gauge symmetries and show that they open up the way to interesting branches of the N=2 moduli space. For some of these models candidates of type-II dual descriptions exist.

scholarly journals Nonsingular bilinear forms on direct sums of ideals

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Beata Rothkegel
Keyword(s):  
Bilinear Form ◽  
Dedekind Domain ◽  
Bilinear Forms ◽  
Direct Sums ◽  
Direct Sum

AbstractIn the paper we formulate a criterion for the nonsingularity of a bilinear form on a direct sum of finitely many invertible ideals of a domain. We classify these forms up to isometry and, in the case of a Dedekind domain, up to similarity.

scholarly journals The integrable (hyper)eclectic spin chain

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Changrim Ahn ◽  
Matthias Staudacher
Keyword(s):  
Spin Chain ◽  
Nearest Neighbor ◽  
Inverse Scattering Method ◽  
Spin Chains ◽  
Scattering Method ◽  
Yang Mills ◽  
Deformation Parameters ◽  
Dilatation Operator ◽  
The One ◽  
State Spin

Abstract We refine the notion of eclectic spin chains introduced in [1] by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians. They turn out to be non-diagonalizable in the multiparticle sector (n > 2), where their “spectrum” consists of an intricate collection of Jordan blocks of arbitrary size and multiplicity. We show how and why the quantum inverse scattering method, sought to be universally applicable to integrable nearest-neighbor spin chains, essentially fails to reproduce the details of this spectrum. We then provide, for n=3, detailed evidence by a variety of analytical and numerical techniques that the spectrum is not “random”, but instead shows surprisingly subtle and regular patterns that moreover exhibit universality for generic deformation parameters. We also introduce a new model, the hypereclectic spin chain, where all parameters are zero except for one. Despite the extreme simplicity of its Hamiltonian, it still seems to reproduce the above “generic” spectra as a subset of an even more intricate overall spectrum. Our models are inspired by parts of the one-loop dilatation operator of a strongly twisted, double-scaled deformation of $$ \mathcal{N} $$ N = 4 Super Yang-Mills Theory.

scholarly journals One-loop string corrections to AdS amplitudes from CFT

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul
Keyword(s):  
Stress Tensor ◽  
Analytic Structure ◽  
Position Space ◽  
Yang Mills ◽  
String Corrections ◽  
The One ◽  
Loop Amplitudes

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

Bilinear forms on non-homogeneous Sobolev spaces

2020 ◽  
Vol 32 (4) ◽  
pp. 995-1026
Author(s):  
Carme Cascante ◽  
Joaquín M. Ortega
Keyword(s):  
Sobolev Spaces ◽  
Bilinear Form ◽  
Positive Measure ◽  
Bilinear Forms ◽  
Homogeneous Sobolev Spaces

AbstractIn this paper, we show that if {b\in L^{2}(\mathbb{R}^{n})}, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces {H_{s}^{2}(\mathbb{R}^{n})\times H_{s}^{2}(\mathbb{R}^{n})}, {0<s<1}, by(f,g)\in H_{s}^{2}(\mathbb{R}^{n})\times H_{s}^{2}(\mathbb{R}^{n})\to\int_{% \mathbb{R}^{n}}(\mathrm{Id}-\Delta)^{\frac{s}{2}}(fg)(\mathbf{x})b(\mathbf{x})% \mathop{}\!d\mathbf{x}is continuous if and only if the positive measure {\lvert b(\mathbf{x})\rvert^{2}\mathop{}\!d\mathbf{x}} is a trace measure for {H_{s}^{2}(\mathbb{R}^{n})}.

scholarly journals Progenitors and Hydrodynamics of Type II and lb Supernovae

1996 ◽  
Vol 145 ◽  
pp. 137-147
Author(s):  
S. E. Woosley ◽  
T. A. Weaver ◽  
R. G. Eastman
Keyword(s):  
Black Holes ◽  
Light Curve ◽  
Mass Loss ◽  
Massive Stars ◽  
The Other ◽  
Shock Interaction ◽  
Type Ii ◽  
Residual Hydrogen ◽  
Ordinary Type ◽  
The One

We review critical physics affecting the observational characteristics of those supernovae that occur in massive stars. Particular emphasis is given to 1) how mass loss, either to a binary companion or by a radiatively driven wind, affects the type and light curve of the supernova, and 2) the interaction of the outgoing supernova shock with regions of increasing pr3 in the stellar mantle. One conclusion is that Type II-L supernovae may occur in mass exchanging binaries very similar to the one that produced SN 1993J, but with slightly larger initial separations and residual hydrogen envelopes (∼1 Mʘ and radius ∼ several AU). The shock interaction, on the other hand, has important implications for the formation of black holes in explosions that are, near peak light, observationally indistinguishable from ordinary Type II-p and lb supernovae.

scholarly journals Higgsing towards E-strings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Kimyeong Lee
Keyword(s):  
String Theory ◽  
Gauge Theories ◽  
The Self ◽  
Flavor Symmetry ◽  
Strongly Coupled ◽  
Superconformal Field Theories ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Elliptic Genera ◽  
Linear Sigma Models

Abstract We explore 6d (1, 0) superconformal field theories with SU(3) and SU(2) gauge symmetries which cascade after Higgsing to the E-string theory on a single M5 near an E8 wall. Specifically, we study the 2d $$ \mathcal{N} $$ N = (0, 4) gauge theories which describe self-dual strings of these 6d theories. The self-dual strings can be also viewed as instanton string solitons of 6d Yang-Mills theories. We find the 2d anomaly-free gauge theories for self-dual strings, amending the naive ADHM gauge theories which are anomalous, and calculate their elliptic genera. While these 2d theories respect the flavor symmetry of each 6d SCFT only partially, their elliptic genera manifest the symmetry fully as these functions as BPS index are invariant in strongly coupled IR limit. Our consistent 2d (0, 4) gauge theories also provide new insights on the non-linear sigma models for the instanton strings, providing novel UV completions of the small instanton singularities. Finally, we construct new 2d quiver gauge theories for the self-dual strings in 6d E-string theory for multiple M5-branes probing the E8 wall, and find their fully refined elliptic genera.

scholarly journals Spontaneously Broken Gauge Symmetry in a Bose Gas with Constant Particle Number

2017 ◽  
Vol 16 (01) ◽  
pp. 1750009
Author(s):  
A. Schelle
Keyword(s):  
Gauge Symmetry ◽  
Particle Number ◽  
Present Model ◽  
Phase Distribution ◽  
Equations Of Motion ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Gauge Symmetries ◽  
Non Local ◽  
Bose Einstein

The interplay between spontaneously broken gauge symmetries and Bose–Einstein condensation has long been controversially discussed in science, since the equations of motion are invariant under phase transformations. Within the present model, it is illustrated that spontaneous symmetry breaking appears as a non-local process in position space, but within disjoint subspaces of the underlying Hilbert space. Numerical simulations show that it is the symmetry of the relative phase distribution between condensate and non-condensate quantum fields which is spontaneously broken when passing the critical temperature for Bose–Einstein condensation. Since the total number of gas particles remains constant over time, the global U(1)-gauge symmetry of the system is preserved.

scholarly journals COMMENTS ON REGULARIZATION AMBIGUITIES AND LOCAL GAUGE SYMMETRIES

2005 ◽  
Vol 20 (25) ◽  
pp. 1933-1938 ◽  
Author(s):  
R. CASANA ◽  
B. M. PIMENTEL
Keyword(s):  
Field Theory ◽  
Gauge Symmetry ◽  
Quantum Level ◽  
Local Gauge ◽  
Gauge Symmetries ◽  
Local Gauge Symmetry ◽  
Coupling Parameters

We study the regularization ambiguities in an exact renormalized (1 +1)-dimensional field theory. We show a relation between the regularization ambiguities and the coupling parameters of the theory as well as their role in the implementation of a local gauge symmetry at quantum level.

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