D-term Uplifts in Non-Supersymmetric Heterotic String Models

Recently, we proposed that the one-loop tadpole diagram in perturbative non-supersymmetric heterotic string vacua that contain an anomalous $U(1)$ symmetry, leads to an analog of the Fayet-Iliopoulos $D$-term in $\mathcal{N}=1$ supersymmetric models, and may uplift the vacuum energy from negative to positive value. In this paper, we extend this analysis to new types of vacua, including those with Stringy Scherk-Schwarz (SSS) spontaneous supersymmetry breaking versus those with explicit breaking. We develop a criteria that facilitates the extraction of vacua with Scherk-Schwarz breaking. We develop systematic tools to analyse the T-duality property of some of the vacua and demonstrate them in several examples. The extraction of the anomalous $U(1)$ $D$-terms is obtained in two ways. The first utilises the calculation of the $U(1)$-charges from the partition function, whereas the second utilises the free fermionic classification methodology to classify large spaces of vacua and analyse the properties of the massless spectrum. The systematic classification method also ensures that the models are free from physical tachyons. We provide a systematic tool to relate the free fermionic basis vectors and one-loop Generalised GSO phases that define the string models, to the one-loop partition function in the orbifold representation. We argue that a $D$-term uplift, while rare, is possible for both the SSS class of models, as well as in those with explicit breaking. We discuss the steps needed to further develop the arguments presented here.Comment: 38 pages, 15 figure

Fayet-Iliopoulos D-Term in Non-Supersymmetric Heterotic String Orbifolds

The Fayet-Iliopoulos $D$-term is a common feature in $\mathcal{N}=1$ string vacua that contain an anomalous $U(1)$ gauge symmetry, and arises from a one--loop diagram in string perturbation theory. The same diagram is generated in string vacua in which supersymmetry is broken directly at the string scale, either via spontaneous Scherk-Schwarz breaking, in which case the gravitino mass is determined by the radius of the circle used in the Scherk-Schwarz mechanism, or via explicit supersymmetry breaking by the GSO projections. We analyse the resulting would-be Fayet-Illiopoulos $D$-term in the non-supersymmetric string vacua and its contribution to the vacuum energy. A numerical estimate in an explicit tachyon-free string-derived model suggests that the would-be $D$-term contribution may uplift the vacuum energy to a positive value.Comment: 11 pages, 1 figur

Fayet–Iliopoulos D-term in non-supersymmetric heterotic string orbifolds

The Fayet–Iliopoulos D-term is a common feature in ${\mathcal {N}}=1$ string vacua that contain an anomalous U(1) gauge symmetry, and arises from a one-loop diagram in string perturbation theory. The same diagram is generated in string vacua in which supersymmetry is broken directly at the string scale, either via spontaneous Scherk–Schwarz breaking, in which case the gravitino mass is determined by the radius of the circle used in the Scherk–Schwarz mechanism, or via explicit supersymmetry breaking by the GSO projections. We analyse the resulting would-be Fayet–Illiopoulos D-term in the non-supersymmetric string vacua and its contribution to the vacuum energy. A numerical estimate in an explicit tachyon-free string-derived model suggests that the would-be D-term contribution may uplift the vacuum energy to a positive value.The Fayet-Iliopoulos $D$-term is a common feature in $\mathcal{N}=1$ string vacua that contain an anomalous $U(1)$ gauge symmetry, and arises from a one--loop diagram in string perturbation theory. The same diagram is generated in string vacua in which supersymmetry is broken directly at the string scale, either via spontaneous Scherk-Schwarz breaking, in which case the gravitino mass is determined by the radius of the circle used in the Scherk-Schwarz mechanism, or via explicit supersymmetry breaking by the GSO projections. We analyse the resulting would-be Fayet-Illiopoulos $D$-term in the non-supersymmetric string vacua and its contribution to the vacuum energy. A numerical estimate in an explicit tachyon-free string-derived model suggests that the would-be $D$-term contribution may uplift the vacuum energy to a positive value

<math display="inline"><mi>D</mi></math>-term uplifts in nonsupersymmetric heterotic string models

Recently, we proposed that the one-loop tadpole diagram in perturbative nonsupersymmetric heterotic string vacua that contain an anomalous U(1) symmetry, leads to an analog of the Fayet-Iliopoulos D-term in N=1 supersymmetric models, and may uplift the vacuum energy from negative to positive value. In this paper, we extend this analysis to new types of vacua, including those with stringy Scherk-Schwarz (SSS) spontaneous supersymmetry breaking versus those with explicit breaking. We develop a criteria that facilitates the extraction of vacua with Scherk-Schwarz breaking. We develop systematic tools to analyze the T-duality property of some of the vacua and demonstrate them in several examples. The extraction of the anomalous U(1) D-terms is obtained in two ways. The first utilizes the calculation of the U(1)-charges from the partition function, whereas the second utilizes the free fermionic classification methodology to classify large spaces of vacua and analyze the properties of the massless spectrum. The systematic classification method also ensures that the models are free from physical tachyons. We provide a systematic tool to relate the free fermionic basis vectors and one-loop generalized GSO phases that define the string models, to the one-loop partition function in the orbifold representation. We argue that a D-term uplift, while rare, is possible for both the SSS class of models, as well as in those with explicit breaking. We discuss the steps needed to further develop the arguments presented here.Recently, we proposed that the one-loop tadpole diagram in perturbative non-supersymmetric heterotic string vacua that contain an anomalous $U(1)$ symmetry, leads to an analog of the Fayet-Iliopoulos $D$-term in $\mathcal{N}=1$ supersymmetric models, and may uplift the vacuum energy from negative to positive value. In this paper, we extend this analysis to new types of vacua, including those with Stringy Scherk-Schwarz (SSS) spontaneous supersymmetry breaking versus those with explicit breaking. We develop a criteria that facilitates the extraction of vacua with Scherk-Schwarz breaking. We develop systematic tools to analyse the T-duality property of some of the vacua and demonstrate them in several examples. The extraction of the anomalous $U(1)$$D$-terms is obtained in two ways. The first utilises the calculation of the $U(1)$-charges from the partition function, whereas the second utilises the free fermionic classification methodology to classify large spaces of vacua and analyse the properties of the massless spectrum. The systematic classification method also ensures that the models are free from physical tachyons. We provide a systematic tool to relate the free fermionic basis vectors and one-loop Generalised GSO phases that define the string models, to the one-loop partition function in the orbifold representation. We argue that a $D$-term uplift, while rare, is possible for both the SSS class of models, as well as in those with explicit breaking. We discuss the steps needed to further develop the arguments presented here