scholarly journals WILSON LOOPS IN OPEN STRING THEORY

1988 ◽  
Vol 03 (03) ◽  
pp. 283-287 ◽  
Author(s):  
KIYOSHI SHIRAISHI
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Symmetry Breaking ◽  
Path Integral ◽  
Wilson Loop ◽  
Mass Spectra ◽  
Open String ◽  
Wilson Loops ◽  
Open Strings ◽  
Correct Weight

Wilson loop elements on torus are introduced into the partition function of open strings as Polyakov’s path integral at one-loop level. Mass spectra from compactification and expected symmetry breaking are illustrated by choosing the correct weight for the contributions from annulus and Möbius strip. We show that Jacobi’s imaginary transformation connects the mass spectra with the Wilson loops. The application to thermopartition function and cosmological implications are briefly discussed.

scholarly journals The disk partition function in string theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Lorenz Eberhardt ◽  
Sridip Pal
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Open String ◽  
Infinite Volume ◽  
Conformal Gauge ◽  
Negative Volume

Abstract We investigate the disk partition function for the open string. This is a subtle problem because of the presence of a residual gauge group PSL(2, ℝ) on the worldsheet even after fixing the conformal gauge. It naively has infinite volume and leads to a vanishing answer. We use different methods that all demonstrate that PSL(2, ℝ) effectively behaves like a group with finite negative volume in the path integral, which leads to a simple prescription for the computation of the disk partition function. We apply our findings to give a simple rederivation of the D-brane tensions.

scholarly journals Strong coupling expansion of circular Wilson loops and string theories in AdS5 × S5 and AdS4 × CP3

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Simone Giombi ◽  
Arkady A. Tseytlin
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Strong Coupling ◽  
Strong Coupling Expansion ◽  
Open String ◽  
String Tension ◽  
Natural Generalization ◽  
Wilson Loops ◽  
Coupling Constant ◽  
Higher Genus

Abstract We revisit the problem of matching the strong coupling expansion of the $$ \frac{1}{2} $$ 1 2 BPS circular Wilson loops in $$ \mathcal{N} $$ N = 4 SYM and ABJM gauge theories with their string theory duals in AdS5× S5 and AdS4× CP3, at the first subleading (one-loop) order of the expansion around the minimal surface. We observe that, including the overall factor 1/gs of the inverse string coupling constant, as appropriate for the open string partition function with disk topology, and a universal prefactor proportional to the square root of the string tension T, both the SYM and ABJM results precisely match the string theory prediction. We provide an explanation of the origin of the $$ \sqrt{T} $$ T prefactor based on special features of the combination of one-loop determinants appearing in the string partition function. The latter also implies a natural generalization Zχ ∼ ($$ \sqrt{T}/{g}_{\mathrm{s}} $$ T / g s )χ to higher genus contributions with the Euler number χ, which is consistent with the structure of the 1/N corrections found on the gauge theory side.

scholarly journals Comments on open string with ‘massive’ boundary term

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190748
Author(s):  
Arkady A. Tseytlin
Keyword(s):  
Scattering Amplitudes ◽  
Partition Function ◽  
Gauge Field ◽  
Path Integral ◽  
Open String ◽  
One Dimensional ◽  
Conformally Invariant ◽  
Additional Constant ◽  
The One ◽  
Definition Of

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

scholarly journals Genus zero Gopakumar-Vafa invariants from open strings

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Andrés Collinucci ◽  
Andrea Sangiovanni ◽  
Roberto Valandro
Keyword(s):  
String Theory ◽  
Open String ◽  
Genus Zero ◽  
Zero Modes ◽  
Open Strings ◽  
Crepant Resolutions ◽  
M Theory

Abstract We propose a new way to compute the genus zero Gopakumar-Vafa invariants for two families of non-toric non-compact Calabi-Yau threefolds that admit simple flops: Reid’s Pagodas, and Laufer’s examples. We exploit the duality between M-theory on these threefolds, and IIA string theory with D6-branes and O6-planes. From this perspective, the GV invariants are detected as five-dimensional open string zero modes. We propose a definition for genus zero GV invariants for threefolds that do not admit small crepant resolutions. We find that in most cases, non-geometric T-brane data is required in order to fully specify the invariants.

scholarly journals GAUGE FIELDS ON TORUS AND PARTITION FUNCTION OF STRINGS

1989 ◽  
Vol 04 (02) ◽  
pp. 389-400 ◽  
Author(s):  
A. NAKAMURA ◽  
K. SHIRAISHI
Keyword(s):  
Partition Function ◽  
Wilson Loop ◽  
Open String ◽  
Closed String ◽  
Point Of View ◽  
Gauge Fields ◽  
Partition Functions ◽  
Zero Modes ◽  
Background Fields ◽  
String Theories

In this paper we consider the interrelation between compactified string theories on torus and gauge fields on it. We start from open string theories with background gauge fields and derive partition functions by path integral. Since the effects of background fields and compactification correlate only through string zero modes, we investigate these zero modes. From this point of view, we discuss the Wilson loop mechanism at finite temperature. For the closed string, only a few comments are mentioned.

scholarly journals 5d/6d Wilson loops from blowups

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hee-Cheol Kim ◽  
Minsung Kim ◽  
Sung-Soo Kim
Keyword(s):  
Partition Function ◽  
Wilson Loop ◽  
Bound States ◽  
Field Theories ◽  
Partition Functions ◽  
Wilson Loops ◽  
Supersymmetric Field Theories

Abstract We generalize Nakajima-Yoshioka’s blowup formula to calculate the partition functions counting the spectrum of bound states to half-BPS Wilson loop operators in 5d (and 6d) supersymmetric field theories. The partition function in the presence of a Wilson loop operator on the Ω-background is factorized when put on the blowup $$ \hat{\mathbb{C}} $$ ℂ ̂ 2 into two Wilson loop partition functions under the localization. This structure provides a set of blowup equations for Wilson loop operators. We explain how to formulate the blowup equations and solve them to compute the partition functions of Wilson loop operators. We test this idea by explicitly calculating the Wilson loop partition functions in various 5d/6d field theories and comparing them against known results and expected dualities.

scholarly journals Holographic entanglement entropy, complexity, fidelity susceptibility and hierarchical UV/IR mixing problem in AdS2/open strings

2018 ◽  
Vol 33 (17) ◽  
pp. 1850100 ◽  
Author(s):  
Kazuharu Bamba ◽  
Davood Momeni ◽  
Mudhahir Al Ajmi
Keyword(s):  
String Theory ◽  
Entanglement Entropy ◽  
Open String ◽  
Two Dimensional ◽  
Conformal Invariant ◽  
Open Strings ◽  
Holographic Entanglement Entropy ◽  
Dimensional Version ◽  
Mixing Problem ◽  
Invariant Quantum

In this paper, we will compute the holographic complexity (dual to a volume in AdS), holographic fidelity susceptibility and the holographic entanglement entropy (dual to an area in AdS) in a two-dimensional version of AdS which is dual to open strings. We will explicitly demonstrate that these quantities are well defined, and then argue that a relation for fidelity susceptibility and time should hold in general due to the AdS2 version of the classical Kepler’s principle. We will demonstrate that it holds for AdS2 solution as well as conformal copies metrics in bulk theory of a prescribed dual conformal invariant quantum mechanics which have been obtained in open string theory. We will also show that hierarchical UV/IR mixing exists in boundary string theory through the holographic bulk picture.

scholarly journals The axion quality problem: global symmetry breaking and wormholes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
James Alvey ◽  
Miguel Escudero
Keyword(s):  
String Theory ◽  
Symmetry Breaking ◽  
Global Symmetries ◽  
Open String ◽  
Einstein Gravity ◽  
Current Status ◽  
Global Symmetry ◽  
Quality Problem ◽  
Global Symmetry Group ◽  
The Impact

Abstract Continuous global symmetries are expected to be broken by gravity, which can lead to important phenomenological consequences. A prime example is the threat that this poses to the viability of the Peccei-Quinn solution to the strong CP problem. In this paper, we explore the impact of wormholes as a source of global symmetry breaking by gravity. We review the current status of wormholes and global symmetries and note that, surprisingly, the axion has a quality problem within non-perturbative Einstein gravity. Although these wormholes lead to a large breaking of global symmetries, we show that their effect is nonetheless relevant for the model building of gauge protected axions. We also find wormhole solutions within two scenarios: (i) an extended global symmetry group within Einstein gravity, and (ii) U(1) wormholes within the low-energy limit of an open String Theory. The former allows us to show that the concept of a global symmetry in General Relativity is somewhat ill-defined. The latter illustrates that for motivated values of the string coupling constant, axions appear to have a quality problem within the open String Theory we consider.

scholarly journals MATRIX MODELS AND ONE-DIMENSIONAL OPEN STRING THEORY

1993 ◽  
Vol 08 (20) ◽  
pp. 3599-3614 ◽  
Author(s):  
JOSEPH A. MINAHAN
Keyword(s):  
Free Energy ◽  
String Theory ◽  
Matrix Model ◽  
Scaling Limit ◽  
Open String ◽  
Model Potential ◽  
Boundary Field ◽  
Random Matrix Model ◽  
Open Strings ◽  
The Matrix

We propose a random matrix model as a representation for D = 1 open strings. We show that the model with one flavor of boundary fields is equivalent to N fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the fermions that falls off as 1/(rij)2. We also generalize this theory to contain an arbitrary number of flavors. For an appropriate choice of the matrix model potential the ground state of the system can be found. Using this potential, we calculate the free energy in the double scaling limit and show that the free energy expansion has the expected form for a theory of open and closed strings if the boundary field mass and couplings have a logarithmic divergence. We then examine the critical properties of this theory and show that the length of the boundary around a hole remains finite, even near the critical point. We also argue that unlike critical string theory or a D = 0 theory, the open string coupling constant is a free parameter.

scholarly journals LOOP VARIABLES AND GAUGE INVARIANT EXACT RENORMALIZATION GROUP EQUATIONS FOR CLOSED STRING THEORY

2013 ◽  
Vol 28 (24) ◽  
pp. 1350116 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Open String ◽  
Background Field ◽  
Closed String ◽  
Gauge Transformations ◽  
Open Strings ◽  
Field Formalism ◽  
Exact Renormalization Group

We formulate the Exact Renormalization Group on the string worldsheet for closed string backgrounds. The same techniques that were used for open strings are used here. There are some subtleties. One is that holomorphic factorization of the closed string vertex operators does not hold in the presence of a cutoff on the Euclidean worldsheet. This introduces extra terms in the Lagrangian at the cutoff scale and they turn out to be crucial for implementing gauge invariance. This naive generalization from open string to closed string requires a massive graviton and the gauge symmetry is Abelian, just as in open string theory. Interestingly, it turns out that if one introduces a nondynamical background metric (as in background field formalism) and combines a gauge transformation on the field with a transformation on the coordinates and background metric, the graviton can be massless. Some examples of background coordinate covariant equations are worked out explicitly. A preliminary discussion of massive modes, massive gauge transformations and the role of worldsheet regulator terms is given. Some of the gauge transformations can be given a geometric meaning if space–time is assumed to be complex at some level.

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