PHYSICAL PROPERTIES OF W GRAVITIES AND W STRINGS

1991 ◽  
Vol 06 (33) ◽  
pp. 3055-3069 ◽  
Author(s):  
SUMIT R. DAS ◽  
AVINASH DHAR ◽  
S. KALYANA RAMA
Keyword(s):  
Free Energy ◽  
Physical Properties ◽  
Configuration Space ◽  
Extra Dimension ◽  
Free Field ◽  
Two Dimensional ◽  
Minimal Models ◽  
Critical Dimensions ◽  
Free Field Realization ◽  
Dimensional Gravity

We investigate some basic physical properties of W gravities and W strings, using a free field realization. We argue that the configuration space of W gravities have global characteristics in addition to the Euler characteristic. We identify one such global quantity to be a "monopole" charge and show how this charge appears in the exponents. The free energy would then involve a "θ" parameter. Using a BRST procedure we find all the physical states of W3 and W4 gravities, and show that physical operators are nonsingular composites of the screening charge operators. (The latter are not physical operators for N≥3.) For W strings we show how the W constraints lead to the emergence of a single (and not many) extra dimension coming from the W-gravity sector. By analyzing the resulting dispersion relations we find that both the lower and upper critical dimensions are lowered compared to ordinary two-dimensional gravity. The pure W gravity spectrum reveals an intriguing "numerological" connection with unitary minimal models coupled to ordinary gravity.

scholarly journals The N = 1 super Heisenberg–Virasoro vertex algebra at level zero

2021 ◽  
Author(s):  
Dražen Adamović ◽  
Berislav Jandrić ◽  
Gordan Radobolja
Keyword(s):  
Fock Space ◽  
Free Field ◽  
Virasoro Algebra ◽  
Vertex Algebra ◽  
Verma Modules ◽  
Minimal Models ◽  
Highest Weight ◽  
Level Zero ◽  
Free Field Realization ◽  
Highest Weight Representations

We study the representation theory of the [Formula: see text] super Heisenberg–Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg–Virasoro vertex algebra [D. Adamović and G. Radobolja, Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications, J. Pure Appl. Algebra 219(10) (2015) 4322–4342; D. Adamović and G. Radobolja, Self-dual and logarithmic representations of the twisted Heisenberg–Virasoro algebra at level zero, Commun. Contemp. Math. 21(2) (2019) 1850008; Y. Billig, Representations of the twisted Heisenberg–Virasoro algebra at level zero, Can. Math. Bull. 46(4) (2003) 529–537] to the super case. We calculated all characters of irreducible highest weight representations by investigating certain Fock space representations. Quite surprisingly, we found that the maximal submodules of certain Verma modules are generated by subsingular vectors. The formulas for singular and subsingular vectors are obtained using screening operators appearing in a study of certain logarithmic vertex algebras [D. Adamović and A. Milas, On W-algebras associated to [Formula: see text] minimal models and their representations, Int. Math. Res. Notices 2010(20) (2010) 3896–3934].

scholarly journals Combinatorial formulation of Ising model revisited

2003 ◽  
Vol 25 (1) ◽  
pp. 49-61 ◽  
Author(s):  
G.A.T.F.da Costa ◽  
A. L. Maciel
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Free Field ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Mathematical Relation

In 1952, Kac and Ward developed a combinatorial formulation for the two dimensional Ising model which is another method of obtaining Onsager's famous formula for the free energy per site in the termodynamic limit of the model. Feynman gave an important contribution to this formulation conjecturing a crucial mathematical relation which completed Kac and Ward ideas. In this paper, the method of Kac, Ward and Feynman for the free field Ising model in two dimensions is reviewed in a selfcontained way and Onsager's formula computed.

scholarly journals TOPOLOGICAL FIELD THEORIES AND THE PERIOD INTEGRALS

1993 ◽  
Vol 08 (17) ◽  
pp. 1627-1637 ◽  
Author(s):  
TOHRU EGUCHI ◽  
YASUHIKO YAMADA ◽  
SUNG-KIL YANG
Keyword(s):  
Correlation Functions ◽  
Field Theories ◽  
Two Dimensional ◽  
Minimal Models ◽  
Recursion Relations ◽  
Dimensional Gravity ◽  
Topological Field ◽  
Topological Gravity ◽  
The One ◽  
Topological Theories

We discuss topological Landau-Ginzburg theories coupled to two-dimensional topological gravity. We point out that the basic recursion relations for correlation functions of the two-dimensional gravity have exactly the same form as the Gauss-Manin differential equations for the period integrals of superpotentials. Thus the one-point functions on the sphere of the Landau-Ginzburg theories are given exactly by the period integrals. We discuss various examples, A-D-E minimal models and the c=3 topological theories.

FREE FIELD APPROACH TO D-BRANES IN N=2 SUPERCONFORMAL MINIMAL MODELS

2004 ◽  
Vol 19 (supp02) ◽  
pp. 294-310
Author(s):  
S. E. PARKHOMENKO
Keyword(s):  
Free Field ◽  
Virasoro Algebra ◽  
Minimal Models ◽  
Field Approach ◽  
Free Field Realization

The approach to construction of D-branes in the N=2 superconformal minimal models based on a free-field realization of the N=2 super-Virasoro algebra unitary modules is represented.

BRST QUANTIZATION OF POLYAKOV’S TWO-DIMENSIONAL GRAVITY II

1991 ◽  
Vol 06 (07) ◽  
pp. 1233-1251 ◽  
Author(s):  
KATSUMI ITOH
Keyword(s):  
Physical State ◽  
Brst Quantization ◽  
State Condition ◽  
Two Dimensional ◽  
Minimal Models ◽  
Physical Spectrum ◽  
Dimensional Gravity ◽  
Conformal Gauge ◽  
Decoupling Mechanism ◽  
Quantized String

Two-dimensional supergravity coupled to the supersymmetric minimal models is quantized by the BRST method. We analysed the physical state condition and found that a state allowed in the physical spectrum must be a direct product of primary states in the matter and gravity sectors. The decoupling mechanism of the unphysical modes is quite similar to the first quantized string theory in the RNS formalism. The formula of KPZ for gravitational scaling dimensions is rederived from the physical state condition. This analysis is done in the conformal gauge.

scholarly journals Macroscopic n-loop amplitude for minimal models coupled to two-dimensional gravity. Fusion rules and interactions

1996 ◽  
Vol 471 (1-2) ◽  
pp. 334-360 ◽  
Author(s):  
M. Anazawa ◽  
H. Itoyama
Keyword(s):  
Two Dimensional ◽  
Minimal Models ◽  
Fusion Rules ◽  
Dimensional Gravity ◽  
Loop Amplitude

scholarly journals BOSONIZATION OF A TOPOLOGICAL COSET MODEL AND NON-CRITICAL STRING THEORY

1994 ◽  
Vol 09 (06) ◽  
pp. 541-547 ◽  
Author(s):  
NOBUYOSHI OHTA ◽  
HISAO SUZUKI
Keyword(s):  
String Theory ◽  
Free Field ◽  
Superconformal Algebra ◽  
Minimal Models ◽  
Total Derivative ◽  
Coset Model ◽  
Free Field Realization ◽  
Topological Field ◽  
The Subject ◽  
Coset Models

We analyze the relation between a topological coset model based on super SL(2, R)/U(1) coset and non-critical string theory by using free field realization. We show that the twisted N=2 algebra of the coset model can be naturally transformed into that of non-critical string. The screening operators of the coset models can be identified either with those of the minimal matters or with the cosmological constant operator. We also find that another screening operator, which is intrinsic in our approach, becomes the BRST non-trivial state of ghost number 0 (generator of the ground ring for c=1 gravity). The relation between non-critical strings and topological field theories is the subject of current interest. It has long been suggested that the latter theories describe the unbroken phase of gravity,1 but their precise relation has not been clear. It has been known that the twisting of N=2 superconformal field theory gives rise to topological theory.1,2 This suggests that any non-critical string theories may have hidden N=2 superconformal symmetry. Indeed, several authors have observed that the BRST current and the antighost field b(z) generate an algebra that is quite similar but apparently not identical to the N=2 superconformal algebra.3 It turns out that the BRST current can be modified by total derivative terms so that the antighost and the physical BRST current exactly generate a topologically twisted N=2 superconformal algebra.4,5 This does not identify, however, the structure of the models with N=2 symmetry. Recently, rather non-trivial correspondence between super SL(2, R)k/U(1) coset model6 and c=1 string has been analyzed through twisted N=2 structure. Mukhi and Vafa7 have revealed an amazing correspondence between these two models for k=3. In this letter, we discuss the relation of these models and the generalization of the correspondence to the minimal models coupled to gravity by means of the free field realization. We find that there is another interesting correspondence for k=1. Super SL(2, R)k/U(1) model is described by the bosonic coset model of SL(2, R)k×U(1)/U(1).8 For a representation of SL(2, R)k, we use the following

Two-dimensional topological insulators exfoliated from Na3Bi-like Dirac semimetals

2021 ◽  
Author(s):  
Xiaoqiu Guo ◽  
Ruixin Yu ◽  
Jingwen Jiang ◽  
Zhuang Ma ◽  
Xiuwen Zhang
Keyword(s):  
Physical Properties ◽  
Epitaxial Growth ◽  
Topological Insulators ◽  
2D Materials ◽  
Van Der Waals ◽  
Two Dimensional ◽  
Dirac Semimetals

Topological insulation is widely predicted in two-dimensional (2D) materials realized by epitaxial growth or van der Waals (vdW) exfoliation. Such 2D topological insulators (TI’s) host many interesting physical properties such...

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