scholarly journals The eclectic flavor symmetry of the ℤ2 orbifold

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Alexander Baur ◽  
Moritz Kade ◽  
Hans Peter Nilles ◽  
Saúl Ramos-Sánchez ◽  
Patrick K. S. Vaudrevange
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Particle Physics ◽  
Mirror Symmetry ◽  
Modular Group ◽  
Complex Structure ◽  
Flavor Symmetry ◽  
Two Dimensional ◽  
Flavor Symmetries

Abstract Modular symmetries naturally combine with traditional flavor symmetries and $$ \mathcal{CP} $$ CP , giving rise to the so-called eclectic flavor symmetry. We apply this scheme to the two-dimensional ℤ2 orbifold, which is equipped with two modular symmetries SL(2, ℤ)T and SL(2, ℤ)U associated with two moduli: the Kähler modulus T and the complex structure modulus U. The resulting finite modular group is ((S3× S3) ⋊ ℤ4) × ℤ2 including mirror symmetry (that exchanges T and U) and a generalized $$ \mathcal{CP} $$ CP -transformation. Together with the traditional flavor symmetry (D8× D8)/ℤ2, this leads to a huge eclectic flavor group with 4608 elements. At specific regions in moduli space we observe enhanced unified flavor symmetries with as many as 1152 elements for the tetrahedral shaped orbifold and $$ \left\langle T\right\rangle =\left\langle U\right\rangle =\exp \left(\frac{\pi \mathrm{i}}{3}\right) $$ T = U = exp π i 3 . This rich eclectic structure implies interesting (modular) flavor groups for particle physics models derived form string theory.

scholarly journals Completing the eclectic flavor scheme of the ℤ2 orbifold

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Alexander Baur ◽  
Moritz Kade ◽  
Hans Peter Nilles ◽  
Saúl Ramos-Sánchez ◽  
Patrick K. S. Vaudrevange
Keyword(s):  
Particle Physics ◽  
Mirror Symmetry ◽  
Predictive Power ◽  
Two Dimensional ◽  
Top Down ◽  
Flavor Symmetries ◽  
Flavor Structure ◽  
Modular Transformations ◽  
Kähler Potential ◽  
Matter Fields

Abstract We present a detailed analysis of the eclectic flavor structure of the two-dimensional ℤ2 orbifold with its two unconstrained moduli T and U as well as SL(2, ℤ)T× SL(2, ℤ)U modular symmetry. This provides a thorough understanding of mirror symmetry as well as the R-symmetries that appear as a consequence of the automorphy factors of modular transformations. It leads to a complete picture of local flavor unification in the (T, U) modulus landscape. In view of applications towards the flavor structure of particle physics models, we are led to top-down constructions with high predictive power. The first reason is the very limited availability of flavor representations of twisted matter fields as well as their (fixed) modular weights. This is followed by severe restrictions from traditional and (finite) modular flavor symmetries, mirror symmetry, $$ \mathcal{CP} $$ CP and R-symmetries on the superpotential and Kähler potential of the theory.

scholarly journals PERTURBATIVE VACUA FROM IIB MATRIX MODEL

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2279-2280
Author(s):  
HIKARU KAWAI ◽  
MATSUO SATO
Keyword(s):  
String Theory ◽  
Path Integral ◽  
Matrix Model ◽  
Moduli Space ◽  
Two Dimensional ◽  
Reduced Models ◽  
Yang Mills ◽  
Large N ◽  
Super Yang Mills Theory

It has not been clarified whether a matrix model can describe various vacua of string theory. In this talk, we show that the IIB matrix model includes type IIA string theory1. In the naive large N limit of the IIB matrix model, configurations consisting of simultaneously diagonalizable matrices form a moduli space, although the unique vacuum would be determined by complicated dynamics. This moduli space should correspond to a part of perturbatively stable vacua of string theory. Actually, one point on the moduli space represents type IIA string theory. Instead of integrating over the moduli space in the path-integral, we can consider each of the simultaneously diagonalizable configurations as a background and set the fluctuations of the diagonal elements to zero. Such procedure is known as quenching in the context of the large N reduced models. By quenching the diagonal elements of the matrices to an appropriate configuration, we show that the quenched IIB matrix model is equivalent to the two-dimensional large N [Formula: see text] super Yang-Mills theory on a cylinder. This theory is nothing but matrix string theory and is known to be equivalent to type IIA string theory. As a result, we find the manner to take the large N limit in the IIB matrix model.

scholarly journals Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Sergei Alexandrov ◽  
Ashoke Sen ◽  
Bogdan Stefański
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Large Volume ◽  
Mirror Symmetry ◽  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Perfect Agreement ◽  
Type Iib String Theory

Abstract We compute the contribution of Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds to the metric on the hypermultiplet moduli space in the large volume, weak coupling limit. Our results are in perfect agreement with the predictions based on S-duality, mirror symmetry and supersymmetry.

scholarly journals D-instantons in Type IIA string theory on Calabi-Yau threefolds

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Sergei Alexandrov ◽  
Ashoke Sen ◽  
Bogdan Stefański
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Mirror Symmetry ◽  
Homology Class ◽  
World Sheet ◽  
Perfect Agreement ◽  
Duality Symmetry ◽  
To Receive ◽  
Perturbative Corrections

Abstract Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.

P-LOOP VACUUM AMPLITUDE IN THE OPEN BOSONIC STRING THEORY

1988 ◽  
Vol 03 (05) ◽  
pp. 511-516 ◽  
Author(s):  
I.D. VAISBURD
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Modular Group ◽  
Open String ◽  
Bosonic String ◽  
The Real ◽  
String Amplitude ◽  
Bosonic String Theory

P-loop open string amplitude is constructed as the integral over the real section of the moduli space. The modular group of the open string is presented.

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

scholarly journals 5d and 4d SCFTs: canonical singularities, trinions and S-dualities

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Cyril Closset ◽  
Simone Giacomelli ◽  
Sakura Schäfer-Nameki ◽  
Yi-Nan Wang
Keyword(s):  
String Theory ◽  
Field Theories ◽  
Flavor Symmetry ◽  
Crepant Resolution ◽  
Superconformal Field Theories ◽  
Hypersurface Singularities ◽  
Canonical Singularities ◽  
Type Iib String Theory ◽  
M Theory

Abstract Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of ‘trinion’ singularities which exhibit these properties. In Type IIB, they give rise to 4d $$ \mathcal{N} $$ N = 2 SCFTs that we call $$ {D}_p^b $$ D p b (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d $$ \mathcal{N} $$ N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as ‘ugly’ components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver ‘bad’. We propose a way to redeem the badness of these quivers using a class $$ \mathcal{S} $$ S realization. We also discover new S-dualities between different $$ {D}_p^b $$ D p b (G)-trinions. For instance, a certain E8 gauging of the E8 Minahan-Nemeschansky theory is S-dual to an E8-shaped Lagrangian quiver SCFT.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Weak gravity bounds in asymptotic string compactifications

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Brice Bastian ◽  
Thomas W. Grimm ◽  
Damian van de Heisteeg
Keyword(s):  
Black Holes ◽  
Moduli Space ◽  
Mass Formula ◽  
Complex Structure ◽  
Mass Ratio ◽  
De Sitter ◽  
String Compactifications ◽  
Type Iib String Theory ◽  
Bps States ◽  
Weak Gravity

Abstract We study the charge-to-mass ratios of BPS states in four-dimensional $$ \mathcal{N} $$ N = 2 supergravities arising from Calabi-Yau threefold compactifications of Type IIB string theory. We present a formula for the asymptotic charge-to-mass ratio valid for all limits in complex structure moduli space. This is achieved by using the sl(2)-structure that emerges in any such limit as described by asymptotic Hodge theory. The asymptotic charge-to-mass formula applies for sl(2)-elementary states that couple to the graviphoton asymptotically. Using this formula, we determine the radii of the ellipsoid that forms the extremality region of electric BPS black holes, which provides us with a general asymptotic bound on the charge-to-mass ratio for these theories. Finally, we comment on how these bounds for the Weak Gravity Conjecture relate to their counterparts in the asymptotic de Sitter Conjecture and Swampland Distance Conjecture.

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