scholarly journals THE ORBIFOLD-STRING THEORIES OF PERMUTATION-TYPE II: CYCLE DYNAMICS AND TARGET SPACE–TIME DIMENSIONS

2010 ◽  
Vol 25 (30) ◽  
pp. 5487-5515
Author(s):  
M. B. HALPERN
Keyword(s):  
Physical State ◽  
Central Charge ◽  
Space Time ◽  
Target Space ◽  
Twisted Sector ◽  
Time Dimension ◽  
State Problem ◽  
Dimension Formula ◽  
Charge Formula ◽  
String Theories

We continue our discussion of the general bosonic prototype of the new orbifold-string theories of permutation-type. Supplementing the extended physical-state conditions of the previous paper, we construct here the extended Virasoro generators with cycle central charge [Formula: see text], where fj(σ) is the length of cycle j in twisted sector σ. We also find an equivalent, reduced formulation of each physical-state problem at reduced cycle central charge cj(σ) = 26. These tools are used to begin the study of the target space–time dimension [Formula: see text] of cycle j in sector σ, which is naturally defined as the number of zero modes (momenta) of each cycle. The general model-dependent formulae derived here will be used extensively in succeeding papers, but are evaluated in this paper only for the simplest case of the "pure" permutation orbifolds.

scholarly journals THE ORBIFOLD-STRING THEORIES OF PERMUTATION-TYPE III: LORENTZIAN AND EUCLIDEAN SPACE—TIMES IN A LARGE EXAMPLE

2011 ◽  
Vol 26 (13) ◽  
pp. 2199-2231
Author(s):  
M. B. HALPERN
Keyword(s):  
Space Time ◽  
Target Space ◽  
Permutation Groups ◽  
Twisted Sector ◽  
Time Dimension ◽  
Dimension Formula ◽  
Time Symmetry ◽  
Time Signature ◽  
The Many ◽  
String Theories

To illustrate the general results of the previous paper, we discuss here a large concrete example of the orbifold-string theories of permutation-type. For each of the many subexamples, we focus on evaluation of the target space–time dimension[Formula: see text], the target space–time signature and the target space–time symmetry of each cycle j in each twisted sector σ. We find in particular a gratifying space–time symmetry enhancement which naturally matches the space–time symmetry of each cycle to its space–time dimension. Although the orbifolds of ℤ2-permutation-type are naturally Lorentzian, we find that the target space–times associated with larger permutation groups can be Lorentzian, Euclidean and even null [Formula: see text], with varying space–time dimensions, signature and symmetry in a single orbifold.

SUPERCONFORMAL ORBIFOLDS INVOLVING THE FERMION NUMBER OPERATOR

2004 ◽  
Vol 19 (22) ◽  
pp. 3637-3667 ◽  
Author(s):  
KATRIN WENDLAND
Keyword(s):  
Central Charge ◽  
Space Time ◽  
Field Theories ◽  
Two Dimensional ◽  
Number Operator ◽  
Superconformal Field Theories ◽  
Fermion Number ◽  
Multicritical Points ◽  
Arbitrary Dimensions ◽  
Charge Formula

We consider orbifolds of two-dimensional unitary toroidal superconformal field theories with target spaces of arbitrary dimensions, where the orbifold group involves the space–time fermion number operator. We construct all so-called superaffine, orbifold prime and super-M-orbifold models by generalizing the constructions of Dixon, Ginsparg and Harvey. We also correct claims made by Dixon, Ginsparg and Harvey about multicritical points among those models with central charge [Formula: see text].

ON THE INTERPOLATING SOLUTIONS OF STRING IN DIFFERENT BACKGROUNDS

1992 ◽  
Vol 07 (15) ◽  
pp. 1361-1366 ◽  
Author(s):  
SUDIPTA MUKHERJI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
String Theory ◽  
Central Charge ◽  
Space Time ◽  
Time Dependent ◽  
Target Space ◽  
Conformal Field ◽  
Β Function ◽  
Time Dependent Solution

We analyze the β-function equations for string theory in the case when the target space has one space-like (or time-like) direction and the rest is some conformal field theory (CFT) with appropriate central charge and has one nearly marginal operator. We show there always exists a space-(time) dependent solution which interpolates between the original background and the background where CFT is replaced by a new conformal field theory, obtained by perturbing CPT by the nearly marginal operator.

scholarly journals THE ORBIFOLDS OF PERMUTATION-TYPE AS PHYSICAL STRING SYSTEMS AT MULTIPLES OF c = 26 II: THE TWISTED BRST SYSTEMS OF ${\hat c} = 52$ MATTER

2007 ◽  
Vol 22 (25) ◽  
pp. 4587-4602 ◽  
Author(s):  
M. B. HALPERN
Keyword(s):  
Physical State ◽  
Central Charge ◽  
Diffeomorphism Groups ◽  
Operator String ◽  
String Theories

This is the second in a series of papers which consider the orbifolds of permutation-type as candidates for new physical string systems at higher central charge. In the first paper, I worked out the extended actions of the twisted sectors of those orbifolds — which exhibit new permutation-twisted worldsheet gravities and correspondingly extended diffeomorphism groups. In this paper I begin the study of these systems as operator string theories, limiting the discussion for simplicity to the strings with [Formula: see text] matter (which are those governed by ℤ2-twisted permutation gravity). In particular, I present here a construction of the twisted reparametrization ghosts and new twisted BRST systems of all [Formula: see text] strings. The twisted BRST systems also imply new extended physical state conditions, whose analysis for individual [Formula: see text] strings is deferred to the next paper of the series.

scholarly journals Mixed Models: Combining incompatible scalar models in any space–time dimension

2017 ◽  
Vol 32 (01) ◽  
pp. 1750001
Author(s):  
John R. Klauder
Keyword(s):  
Quantum Theory ◽  
Mixed Models ◽  
Specific Interaction ◽  
Free Action ◽  
General Rule ◽  
Space Time ◽  
Time Dimension ◽  
Classical Action ◽  
Dimension Formula ◽  
Special Cases

Traditionally, covariant scalar field theory models are either super renormalizable, strictly renormalizable, or nonrenormalizable. The goal of “Mixed Models” is to make sense of sums of these distinct examples, e.g. [Formula: see text], which includes an example of each kind for space–time dimension [Formula: see text]. We show how the several interactions such mixed models have may be turned on and off in any order without any difficulties. Analogous results are shown for [Formula: see text], etc. for all [Formula: see text]. Different categories hold for [Formula: see text] such as, e.g. [Formula: see text], that involve polynomial [Formula: see text] and suitable nonpolynomial [Formula: see text] interactions, etc. Analogous situations for [Formula: see text] (time alone) offer simple “toy” examples of how such mixed models may be constructed. As a general rule, if the introduction of a specific interaction term reduces the domain of the free classical action, we invariably find that the introduction of the associated quantum interaction leads, effectively, to a “nonrenormalizable” quantum theory. However, in special cases, a classical interaction that does not reduce the domain of the classical free action may generate an “unsatisfactory” quantum theory, which generally involves a model-specific, different approach to become “satisfactory.” We will encounter both situations in our analysis.

scholarly journals GENERALIZED W3-STRINGS FROM FREE FIELDS

1995 ◽  
Vol 10 (06) ◽  
pp. 515-524 ◽  
Author(s):  
J. M. FIGUEROA-O'FARRILL ◽  
C. M. HULL ◽  
L. PALACIOS ◽  
E. RAMOS
Keyword(s):  
Bosonic Strings ◽  
Free Field ◽  
Space Time ◽  
General Construction ◽  
Special Cases ◽  
Free Fields ◽  
Rule Out ◽  
General Conditions ◽  
String Theories

The conventional quantization of w3-strings gives theories which are equivalent to special cases of bosonic strings. We explore whether a more general quantization can lead to new generalized W3-string theories by seeking to construct quantum BRST charges directly without requiring the existence of a quantum W3-algebra. We study W3-like strings with a direct space-time interpretation — that is, with matter given by explicit free field realizations. Special emphasis is placed on the attempt to construct a quantum W-string associated with the magic realizations of the classical w3-algebra. We give the general conditions for the existence of W3-like strings, and comment on how the known results fit into our general construction. Our results are negative: we find no new consistent string theories, and in particular rule out the possibility of critical strings based on the magic realizations.

scholarly journals POLYHOMOGENEOUS SOLUTIONS OF NONLINEAR WAVE EQUATIONS WITHOUT CORNER CONDITIONS

2006 ◽  
Vol 03 (01) ◽  
pp. 81-141 ◽  
Author(s):  
PIOTR T. CHRUŚCIEL ◽  
SZYMON ŁȨSKI
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Space Time ◽  
Einstein Equations ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Cauchy Problems ◽  
Time Dimension ◽  
Wave Maps ◽  
Corner Conditions

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd space-time dimension. In recent work it has been shown that for non-linear wave equations, or for wave maps, polyhomogeneous initial data lead to solutions which are also polyhomogeneous provided that an infinite hierarchy of corner conditions holds. In this paper we show that the result is true regardless of corner conditions.

scholarly journals NEW SUPERSTRING ISOMETRIES AND HIDDEN DIMENSIONS

2007 ◽  
Vol 22 (29) ◽  
pp. 5301-5323 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Extra Dimension ◽  
Isometry Group ◽  
Space Time ◽  
Time Dimension ◽  
Superstring Theory ◽  
Symmetry Transformations ◽  
Noncritical Strings ◽  
A Chain ◽  
Symmetry Generators ◽  
Special Space

We study the hierarchy of hidden space–time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is canceled by that of the ghost part. These symmetries, referred to as the α-symmetries, are induced by special space–time generators, violating the equivalence of ghost pictures. We classify the α-symmetry generators in terms of superconformal ghost cohomologies Hn ~ H-n-2(n≥0) and associate these generators with a chain of hidden space–time dimensions, with each ghost cohomology Hn ~ H-n-2 "contributing" an extra dimension. Namely, we show that each ghost cohomology Hn ~ H-n-2 of noncritical superstring theory in d-dimensions contains d+n+1 α-symmetry generators and the generators from Hk ~ H-k-2, 1≤k ≤n, combined together, extend the space–time isometry group from the naive SO (d, 2) to SO (d+n, 2). In the simplest case of n = 1 the α-generators are identified with the extra symmetries of the 2T-physics formalism, also known to originate from a hidden space–time dimension.

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