MULTILOOP CALCULUS IN P-ADIC STRING THEORY AND BRUHAT-TITS TREES

We treat the open p-adic string world sheet as a coset space F=T/Γ, where T is the Bruhat-Tits tree for the p-adic linear group GL (2, ℚp) and Γ⊂ PGL (2, ℚp) is some Schottky group. The boundary of this world sheet corresponds to p-adic Mumford curve of finite genus. The string dynamics is governed by the local gaussian action on the tree T. We find the amplitudes for emission processes of the tachyon states from the boundary.

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QUANTIZATION OF THE LIOUVILLE MODE AND STRING THEORY

Modern Physics Letters A ◽

10.1142/s0217732389001209 ◽

1989 ◽

Vol 04 (11) ◽

pp. 1033-1041 ◽

Cited By ~ 80

Author(s):

SUMIT R. DAS ◽

SATCHIDANANDA NAIK ◽

SPENTA R. WADIA

Keyword(s):

String Theory ◽

Dimensional Space ◽

Scalar Fields ◽

Space Time ◽

Two Dimensions ◽

General Covariance ◽

World Sheet ◽

Lorentzian Signature ◽

Dimensional Space Time ◽

Background Fields

We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.

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STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE

International Journal of Modern Physics A ◽

10.1142/s0217751x99002116 ◽

1999 ◽

Vol 14 (28) ◽

pp. 4501-4517 ◽

Cited By ~ 1

Author(s):

FEDELE LIZZI

Keyword(s):

String Theory ◽

Dirac Operator ◽

Noncommutative Geometry ◽

Low Energy ◽

Target Space ◽

World Sheet ◽

Crucial Point ◽

Spectral Action ◽

Energy Eigenvalues ◽

The World

We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

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LOOP VARIABLES IN STRING THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x03012126 ◽

2003 ◽

Vol 18 (05) ◽

pp. 767-809 ◽

Cited By ~ 13

Author(s):

B. SATHIAPALAN

Keyword(s):

Renormalization Group ◽

String Theory ◽

Equations Of Motion ◽

Renormalization Group Equation ◽

Group Method ◽

Group Equation ◽

World Sheet ◽

Gauge Invariant ◽

Variable Approach ◽

Exact Renormalization Group

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

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Compactification of string theory on coset space

Chinese Physics Letters ◽

10.1088/0256-307x/5/10/002 ◽

1988 ◽

Vol 5 (10) ◽

pp. 437-440

Author(s):

Tang Jufei ◽

Zhu Chuanjie

Keyword(s):

String Theory ◽

Coset Space

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ON HIGHER-SPIN GENERALIZATIONS OF STRING THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x94000674 ◽

1994 ◽

Vol 09 (09) ◽

pp. 1527-1543 ◽

Cited By ~ 14

Author(s):

H. LU ◽

C. N. POPE ◽

X. J. WANG

Keyword(s):

String Theory ◽

Gauge Field ◽

Virasoro Algebra ◽

Two Dimensional ◽

Minimal Models ◽

World Sheet ◽

The World ◽

Higher Spin ◽

String Theories

We construct BRST operators for certain higher-spin extensions of the Virasoro algebra, in which there is a spin-s gauge field on the world sheet, as well as the spin-2 gauge field corrresponding to the two-dimensional metric. We use these BRST operators to study the physical states of the associated string theories, and show how they are related to certain minimal models.

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VORTICES IN HIGH-TEMPERATURE STRING THEORY

Modern Physics Letters A ◽

10.1142/s0217732389001234 ◽

1989 ◽

Vol 04 (11) ◽

pp. 1063-1067 ◽

Cited By ~ 6

Author(s):

G. CHAPLINE ◽

F.R. KLINKHAMER

Keyword(s):

Phase Transition ◽

Free Energy ◽

High Temperature ◽

String Theory ◽

High Temperatures ◽

World Sheet ◽

Genus Zero ◽

Mass Gap ◽

The World

We discuss the role of XY-like vortices on the world-sheet for the free energy of strings at high temperatures. There is a Kosterlitz-Thouless phase transition at the Hagedorn temperature, above which the vortices contribute to the free energy in genus zero and generate a mass gap. We speculate that high-temperature “string” theory could be essentially discrete.

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D-instantons, string field theory and two dimensional string theory

Journal of High Energy Physics ◽

10.1007/jhep11(2021)061 ◽

2021 ◽

Vol 2021 (11) ◽

Author(s):

Ashoke Sen

Keyword(s):

Field Theory ◽

String Theory ◽

Matrix Model ◽

String Field Theory ◽

Scattering Amplitude ◽

Two Dimensional ◽

World Sheet ◽

Numerical Result ◽

Instanton Contribution ◽

The Matrix

Abstract In [4] Balthazar, Rodriguez and Yin (BRY) computed the one instanton contribution to the two point scattering amplitude in two dimensional string theory to first subleading order in the string coupling. Their analysis left undetermined two constants due to divergences in the integration over world-sheet variables, but they were fixed by numerically comparing the result with that of the dual matrix model. If we consider n-point scattering amplitudes to the same order, there are actually four undetermined constants in the world-sheet approach. We show that using string field theory we can get finite unambiguous values of all of these constants, and we explicitly compute three of these four constants. Two of the three constants determined this way agree with the numerical result of BRY within the accuracy of numerical analysis, but the third constant seems to differ by 1/2. We also discuss a shortcut to determining the fourth constant if we assume the equality of the quantum corrected D-instanton action and the action of the matrix model instanton. This also agrees with the numerical result of BRY.

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The physical states of the Hybrid Formalism

Journal of High Energy Physics ◽

10.1007/jhep10(2021)168 ◽

2021 ◽

Vol 2021 (10) ◽

Author(s):

Matthias R. Gaberdiel ◽

Kiarash Naderi

Keyword(s):

String Theory ◽

Free Field ◽

Vertex Operators ◽

World Sheet ◽

Brst Cohomology ◽

The World ◽

The Way

Abstract String theory on AdS3 × S3 × $$ \mathbbm{T} $$ T 4 with one unit (k = 1) of NS-NS flux is considered in the hybrid formalism of Berkovits, Vafa & Witten (BVW). Using the free field realisation of the world-sheet theory at k = 1, we identify explicitly the BRST cohomology classes corresponding to some of the low-lying states of the dual CFT. In particular, we do this for the $$ \mathcal{N} $$ N = 4 superconformal generators of the symmetric orbifold theory, and we confirm these identifications by showing that the worldsheet correlators reproduce the expected dual CFT answer. Along the way we note that the physical vertex operators on the worldsheet have a simpler form if one works with a different, but equivalent, choice for the BRST operators relative to BVW.

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