RG flows and cascades of $Li{f}_4^{(2)}\times S^1\times S^5$ vacua

The (F1,D2,D8) brane configuration produces $Lif_4^{(2)}\times {S}^1\times S^5$Lifshitzvacuasupportedby\mathrm{‘}massiv{e}^{\mathrm{\prime }}$B$-field. We present exact deformations of this system under which new massless $B$-modes of strings also get excited. Due to these massless modes the deformed solutions flow to conformally $Li{f}_4^{(3)}\times S^1\times S^5$ vacua in the IR. The latter types are supersymmetric solutions of ordinary type IIA theory. The massive and massless $B_{\mu \nu }$ modes segregate out in the IR. We confirm that the massive $B$ mode and cosmological constant indeed decouple from the theory rendering the IR field dynamics controlled by massless fields only. A similar effect is observed on the UV side of the flow where a relativistic regime reappears. We also present cascading' Lifshitz vacua in which dynamical exponent has integral jumps along the flow, $Lif_4^{(3)}\to Lif_4^{(2)}\to Lif_4^{(1)}$. The critical $Lif_4^{(2)}$ theory separates deconfining’ $Li{f}_4^{(3)}$ IR theory from the confining Yang-Mills phase in UV.