scholarly journals INTERACTIONS OF DISCRETE STATES WITH NONZERO GHOST NUMBER IN c = 1 2D GRAVITY

1992 ◽  
Vol 07 (29) ◽  
pp. 2723-2730 ◽  
Author(s):  
NOBUYOSHI OHTA ◽  
HISAO SUZUKI
Keyword(s):  
Quantum Gravity ◽  
Vertex Operator ◽  
Effective Action ◽  
2D Gravity ◽  
Ghost Number ◽  
Two Dimensional ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving ◽  
Operator Representations

We study the interactions of the discrete states with nonzero ghost number in c = 1 two-dimensional (2D) quantum gravity. By using the vertex operator representations, it is shown that their interactions are given by the structure constants of the group of the area preserving diffeomorphism similar to those of vanishing ghost number. The effective action for these states is also worked out. The result suggests that the whole system has a BRST-like symmetry.

scholarly journals INTERACTION OF DISCRETE STATES IN TWO-DIMENSIONAL STRING THEORY

1991 ◽  
Vol 06 (35) ◽  
pp. 3273-3281 ◽  
Author(s):  
I. R. KLEBANOV ◽  
A. M. POLYAKOV
Keyword(s):  
String Theory ◽  
Effective Action ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving

We study the couplings of discrete states that appear in the string theory embedded in two dimensions, and show that they are given by the structure constants of the group of area preserving diffeomorphisms. We propose an effective action for these states, which is itself invariant under this infinite-dimensional group.

scholarly journals NEW DISCRETE STATES IN TWO-DIMENSIONAL SUPERGRAVITY

2007 ◽  
Vol 22 (07) ◽  
pp. 1375-1394 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Operator Algebra ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Field Theories ◽  
Two Dimensional ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving ◽  
Volume Preserving ◽  
Lowering Operator

Two-dimensional string theory is known to contain the set of discrete states that are the SU (2) multiplets generated by the lowering operator of the SU (2) current algebra. Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. In this paper we show that the interaction of d = 2 superstrings with the superconformal β - γ ghosts enlarges the actual algebra of the dimension 1 currents and hence the new ghost-dependent discrete states appear. Generally, these states are the SU (N) multiplets if the algebra includes the currents of ghost numbers n : -N ≤ n ≤ N - 2, not related by picture changing. We compute the structure constants of these ghost-dependent discrete states for N = 3 and express them in terms of SU (3) Clebsch–Gordan coefficients, relating this operator algebra to the volume preserving diffeomorphisms in d = 3. For general N, the operator algebra is conjectured to be isomorphic to SDiff (N). This points at possible holographic relations between two-dimensional superstrings and field theories in higher dimensions.

THE APPEARANCE OF MATTER FIELDS FROM QUANTUM FLUCTUATIONS OF 2D-GRAVITY

1989 ◽  
Vol 04 (22) ◽  
pp. 2125-2139 ◽  
Author(s):  
V.A. KAZAKOV
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Critical Exponent ◽  
2D Gravity ◽  
Central Charge ◽  
Quantum Fluctuations ◽  
Two Dimensional ◽  
Conformal Fields ◽  
Exactly Solvable ◽  
Matter Fields

It is established that various critical regimes may occur for a model of two-dimensional pure quantum gravity. These regimes correspond to the presence of effective fields with scaling dimensions Δk=−γ str ·k/2, k=1, 2, 3 ..., where γ str =−1/m, m=2, 3, 4 ... is the critical exponent of “string susceptibility” (with respect to the cosmological constant). This behaviour is typical for unitary conformal fields with the central charge c=1−6/m(m+1) in the presence of 2D-quantum gravity. We use the framework of loop equations for the invariant boundary functional, which are exactly solvable in this case.

scholarly journals 2D QUANTUM GRAVITY COUPLED TO RENORMALIZABLE MATTER FIELDS

1994 ◽  
Vol 09 (32) ◽  
pp. 5689-5709 ◽  
Author(s):  
JAN AMBJØRN ◽  
KAZUO GHOROKU
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Effective Action ◽  
Two Dimensional ◽  
Conformally Invariant ◽  
Renormalization Group Equations ◽  
Β Function ◽  
Matter Fields

We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable but not conformally invariant. Questions concerning the β function and the effective action are addressed, and the effective action and the dressed renormalization group equations are determined for various matter potentials.

scholarly journals INTERACTION OF d=2, c=1 DISCRETE STATES FROM STRING FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 2167-2176 ◽  
Author(s):  
I. YA. AREF’EVA ◽  
P.B. MEDVEDEV ◽  
A.P. ZUBAREV
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Effective Action ◽  
2D Gravity ◽  
Ward Identities ◽  
Discrete States ◽  
Pole Structure

Starting from string field theory for 2D gravity coupled to c=1 matter we analyze the off-shell tree amplitudes of discrete states. The amplitudes exhibit the pole structure and we use the off-shell calculus to extract the residues and prove that only the residues are constrained by the Ward identities. The residues generate a simple effective action.

scholarly journals D = 26 AND EXACT SOLUTION TO THE CONFORMAL-GAUGE TWO-DIMENSIONAL QUANTUM GRAVITY

1999 ◽  
Vol 14 (04) ◽  
pp. 521-536 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Field Equation ◽  
Quantum Gravity ◽  
Critical Dimension ◽  
Bosonic String ◽  
Ghost Number ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Heisenberg Picture ◽  
Conformal Gauge

The conformal-gauge two-dimensional quantum gravity is formulated in the framework of the BRS quantization and solved completely in the Heisenberg picture: all n-point Wightman functions are explicitly obtained. The field-equation anomaly is shown to exist as in other gauges, but there is no other subtlety. At the critical dimension D = 26 of the bosonic string, the field-equation anomaly is shown to be absent. However, this result is not equivalent to the statement that the conformal anomaly is proportional to D - 26. The existence of the FP-ghost number current anomaly is seen to be an illusion.

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